Few electric bicycles have regenerative braking. Most quality e-bikes seem to be settling on mid-drive, which even makes regenerative braking impossible because there is a freewheel between the wheel and the drive, and the rear derailleur as the chain tensioner!
Why is this the case? Why are regenerative brakes rare?
There are several reasons for regenerative brakes not being common on bicycles unlike in electric cars:
Electric bicycles have very poor acceleration, and the rider produces about half of the acceleration with the motor producing the rest. The power is limited by the low-speed motor, not the battery. Most quality electric motors like to spin at 5000 - 20000 RPM, but in e-bikes they do not spin at any such speed range. The best RPM situation in electric bikes is in mid-drive bikes that have enough space to use reduction gears, and the mid-drive arrangement does not allow regenerative braking due to the freewheel. The worst RPM situation in electric bikes (lowest RPM) is in hub motors, the only arrangement that would make regenerative braking possible. These hub motors cannot produce high forwards torque, and therefore, cannot produce high inverse torque for braking. In contrast, electric cars are well-known for their high acceleration, thus allowing rapid braking. An electric bicycle with regenerative braking could produce only half of its poor acceleration as braking force, and it is not at all significant.
A common use case for regenerative braking in electric cars is going downhill. Most car drivers drive always very near the speed limit (unless traffic condition or safety requires otherwise). In contrast, most bicyclists ride at a very low speed that could be much higher. A car driver going downhill needs to brake to keep under the speed limit, whereas a bicyclist often uses a downhill as an opportunity for going fast. The most common braking at downhills for bicyclists is a 90-degree or hairpin turn after a downhill, and to maximize average speed, most bicyclists only brake very close to the turn, instead of braking all the time before the turn. Thus, a downhill is not a good location for an electric bicyclist to brake.
Another common use case for regenerative braking in electric cars is stopping at a red light. In contrast to cars where braking close to red lights instead of anticipating the traffic lights far away is common even for internal combustion engine cars lacking regenerative braking, most bicyclists have learned an energy-saving way of going through traffic lights, avoiding unnecessary accelerations to high speeds only to need to brake right away. While a regenerative brake could be useful for an electric bicyclist adopting a different rapid start - rapid stop riding style, most bicyclists do not consider such a riding style necessary.
The final killing blow making regenerative braking infeasible is the controlling of such brakes. In most cars, there is natural engine braking. Some electric or hybrid-electric cars (Toyota) simulate the typical engine braking amount with regenerative braking, while at the same time having complicated (expensive, heavy) machinery to adapt between regenerative braking and disc braking using the brake pedal. This approach has the advantage of familiarity for most automatic transmission car drivers. Such an expensive, complicated and heavy machine would not be acceptable on a bicycle. Other electric cars (Tesla) cheat somewhat and make the engine braking huge, to avoid having the complicated (expensive, heavy) machinery to adapt between regenerative braking and disc braking when the driver presses the brake pedal. In contrast, high-quality bicycles have extremely low rolling resistance and no engine braking -- there is a freewheel. The natural slight regenerative braking would be of no value in such a bicycle. The braking controls of a high-quality bicycle are independent levers for front and rear wheels. A regenerative brake would work on only one of those levers. Most of the time, the bicyclist uses the front brake only, and most quality hub motor electric bicycles are not front wheel drive for a good reason (when going uphill seated, the front wheel is practically unloaded and would slip). Even for a bicyclist that brakes with the rear brake, there would need to be complicated (expensive, heavy) machine to operate both the regenerative brake and the disc/rim brake with the same lever. Cyclists would not find such a piece of machinery acceptable. Thus, the only way to make regenerative braking possible would be to add a third regenerative brake only control working only for the rear brake. It would be a terrible brake due to the low torque of hub motor drive. Such a brake would be unused for most of the time.
Also, to produce useful torque at low weight, an electric motor needs to spin fast. The only arrangement making the drive motor spin fast on an e-bike is mid-drive, where the motor drives the bottom bracket through reduction gears. Such an arrangement does not work with regenerative brakes due to rear derailleur being the chain tensioner, and due to the freewheel in the rear wheel.
Because regenerative brakes have terribly low power (reason #1), no valid use case (reasons #2 and #3) and no feasible means of control (reason #4), and because mid-drive is the most logical drive variant in e-bikes that makes regenerative braking impossible, regenerative brakes are not feasible on e-bikes unlike they are in electric cars.
Most bicycling energy goes toward overcoming wind resistance, especially for casual riders. That energy is lost, with no chance for regeneration.
Liberty Trike claims that the most you can expect to gain from regeneration is 5-10% of energy expended. Panda eBikes claims 10%, with some math.
By comparison, an electric car or truck has a lot more mass and momentum. This makes regenerative braking more worthwhile. These sorts of e-vehicles also often have more sophisticated battery thermal management, which makes it safer and more efficient to quickly dump energy back into the battery.
Energy grows with the square of speed. If you are a normal weight cyclist (70 kg) with a heavy e-bike (30 kg), riding at 25.2 km/h (7 m/s), you will have an energy of
E = m * v^2 / 2 = 100 kg * (7 m/s)^2 / 2 = 2450 J = 2450 Ws
For an e-bike with a 250 W motor, that energy suffices for
t = E/P = 2450 Ws / 250 W = 9.8 s
If you have to stop for a red light every 1 km, you are riding for 1 km/7 m * s = 143 s. I.e., you only get about 7% range extension out of recuperation. I guess, manufacturers will prefer to give you 7% more battery (simple and good for marketing) rather than going through the extra effort of developing a recuperating drive. Especially since the larger battery will serve you well on long distance tours, where the effect of recuperation would be totally negligible.
The above covers the use in fairly flat terrain, which appears to be the major market for e-bikes. However, there are use cases that would indeed favor adding a regenerative brake:
Recuperation would be nice for commuting through a city. In such a setting it might be worth riding with an empty battery, and only using the recovered energy to accelerate when the lights change. It would be possible to build some really light e-bike on that principle (only a tiny battery for roughly 5 kWs), but that's not the main market for e-bikes: Normal use is to ride with a full battery and stop before the battery becomes empty.
Recuperation could be a game-changer in hilly terrain: 100 m elevation translate to
E = g*m*h = 9.81 m/s^2 * 100 kg * 100 m = 98.1 kWs
which is energy that needs to be expended on the ascent, and which needs to be removed on the descent. Recovering it on the descent for the next ascent would indeed be a very significant advantage.
However, there's a catch: People ride downhill pretty fast. If our standard biker rides down a slope of 5% at 54 km/h (15 m/s), their weight has a power output of
P = 5% * g*v*m = 0.05 * 9.81 m/s^2 * 15 m/s * 100 kg = 736 W
That's almost three times the power rating of a typical e-bike motor. And I used a rather benign example, I have done descents that produced about 2 kW. To make this sort of recuperation feasible, the electric motor would need to be built much stronger than it is allowed to be. It would need to be roughly five times as large and be limited electronically to output only 250 W while accelerating. I think, it's obvious why e-bike manufacturers do not do this.
Juhist made some good points, but none of them are really show-stoppers.
First off, clearly regenerative brakes are only useful when you actually use them sufficiently much. Well, it turns out cyclists don't like to brake – which makes sense because normally it's just wasted energy/time, and unnecessary pad-wear. In relatively flat settings, there's nothing to be gained from braking at one place to get a boost in another, whereas on mountain roads or prepared MTB tracks, we're happy to just get a really high speed out of the decents, and with increasing speed air drag becomes much stronger so then there's not much left for regen. However, if one were disciplined enough to use the regen brakes all the way on the downhill passages (and maybe even continue pedalling lightly), then you would get back nearly all the energy for the next ascent, because electric motors and batteries are pretty efficient.
Of course that would mean going down you wouldn't be much faster than going up, which I guess most cyclists would feel as taking the satisfaction away from the downhill passages. (I personally find it much more satisfying to arrive at a mountaintop knowing all the energy came from my legs, but I seem to be in a minority there.)
Where the situation is a bit different is in MTB on natural singletrails. Anyone but downhill racers will tackle these with a lot of braking anyway because it's just too dangerous to go down very fast. But unfortunately, in MTBs hub motors are particularly problematic because they don't offer as much torque and add unsprung mass, whereas mid-motors aren't capable of regen braking.
IMO regenerative braking has one place where it really should be popular, and definitely would work well: long distance touring on mountainous roads. Time doesn't matter much there – taking longer for the descents is actually a welcome break and opportunity to see more of the nature; also you need to be extra careful when hours away from any help in event of a crash. The extra mass of the baggage would also add to the energy that can be reclaimed, whereas the unsprung mass of a hub motor becomes insignificant.
Common wisdom seems to be that e-bikes don't make sense at all for long-distance as there's nowhere to charge, but properly implemented regen braking is exactly what would make it sensible – if the cyclist is willing to actually use it in braking mode as much as in power mode.
We can identify scenarios where recuperation could help a lot:
The article argues that someone who is not a fit biker (but e.g. an elderly person doing their shopping) may easily have the muscle power to go at an acceptable speed in the flat once at speed, but they may have difficulties producing the power output to accelerate the bike/hold the speed uphill that allows a safe and stable operation of the bike.
In fact, they basically argue for an electrically assisted system that helps only at low speed - while not hindering the normal muscle output above that speed. The idea is to get rid of peak power, so the biker can get along with their own continuous lower power output.
Hills need some more power stored than acceleration after a stop, but such a system could get away with very small batteries (see below).
The idea here is very different from sportive e-biking: the assistance is meant solely to help people avoid people becoming so slow that the bike becomes unstable.
The competitor of recuperation is a bigger battery, and IMHO this is where it is not considerd worth while.
A glance through the internet tells me that one can get 1300 kWs (360 Wh) in maybe 5 kg of battery.
Going with @cmaster's back-of-the-envelope calculations, that translates either to 500x accelerating from stand to cruising speed or 1300 m of elevation gain.
With a recuperative system as outlined above, we could get away with a small battery of < 1 kg. Without recuperation, 1 kg of battery using the electical assistance only as outlined above would still give us the equivalent of 250 m elevation gain or 100 starts. Plenty for every-day use (and the scenarion is not to stop pedaling, so this would cut 500 m elevation gain in half or so). But 1 kg battery is still small compared to the weight of the drive. (Yes, with the target clientele of the scenario above, a 1 kg battery instead of a 5 kg may be an argument...)
And 5 kg battery can be marketed as assisting not only for acceleration and getting us to go uphill at maybe 8 or 9 km/h but at getting us to an acceptable overall speed for so many km. And it can be marketed in line with sportive e-bike - which the outlined system would not be.
And incidentally, going assisted all the time will hide the resistance due to big low-pressure (or even knobby) tires and a not-so-very-efficient drive train.
The electricity costs for charging an e-bike for a 18 km ride are in the order of US$0.01–$0.03. Even if you ride 15000 km/year, that's less than $20/year in electricity costs. Apart from all the reasons already mentioned, regenerative breaking on e-bikes is uncommon because the electricity costs for charging and e-bike regularly are negligible compared to the other costs of e-bikes, most notably purchase, depreciation, and maintenance. Most users can recharge every day and would notice no advantage whatsoever from regenerative braking.
