What I've learned:
A: UPSs generally use sealed lead acid batteries, which use a slightly higher voltage to charge. Using an auto battery will result in the battery being in a slight state of overcharge requiring period topping up.
B: UPS inverters are not designed with cooling in mind to run at rated capacity for more than the nominal 15 minutes. Of course oversizing will get you longer run time and a lower percentage of rated capacity. Cooling could be as simple as a thermostat and a small 12v fan, or an oversized box so it had more surface area. (Merit in making it roughly the same footprint as a car battery, with legs that straddle the bumpy bits on the top of the battery)
C: One forum stated that a car battery cannot provide the needed power, averaging only about 150 watts (12v @13 amps) This may be the C/5 or C/20 discharge. A typical auto battery stores about 100 amp hours or about 1.2 kWh. 150 W corresponds to about an 8 hour full discharge or about 4 hours without damaging the battery.
C: A car battery is not robust against repeated flat line discharge.
My experience has been that conventional backup power supplies such as APC™ and Cyber Power™ have MUCH smaller batteries than a car battery, will typically handle their rated power for 15 minutes. Even used infrequently they seldom last more than 2-3 years before they start to complain and want battery replacements, which are much more more expensive per pound than auto batteries. By comparison, the car battery that supplies my backup sump pump typically lasts 5-7 years between replacements.
Seems to me that a unit designed to use an auto battery, while not great for repeated long power outages, would be fine for the frequent short outages that many rural dwellers encounter. Properly designed, it may be possible to switch batteries on the fly using a double pole make before break. This would result in a short time where the fully charged battery would attempt to charge the used battery.
BUT so far I've been unable to 'divorce' the charge/inverter/filter function from the energy storage function in a consumer product. I'd like to understand why not.
Edit: So additional background.
The replacement battery for an APC Back-UPS Pro 1500 costs $US130 and weighs 12.8 lbs. After market ones run about 2/3 of this.
A Silverado battery at Costco costs US 116, and weighs 37 lbs. My experience with my truck suggests that a battery can be run to zero a dozen or so times and still hold enough charge to start the truck in winter.
I have a 12 v sump pump with an open cell marine battery on it. The house has an overall air change time of under 3 hours. Gas accumulation seems unlikely. As to acid droples (referencing another post, it has a plastic box, with a non-tight lid, and the top of the battery is sprinkled with baking soda. The soda is my addition. The product is intended for not very well ventilated basements.