If I can get a good drink free of charge, why should I pay for any drinks? Quark's customers can always get the food and drinks free of charge from the replicator. It is after all a post-scarcity world.
Why is Quark's bar always so crowded? I can understand one or two suckers among his customers once in a while but his bar is always crowded. What is the secret to his business success given the fatal flaw in the business model, thanks to replicators?
In the UK, you can easily get three or four beers in a supermarket for the price of one drink in a pub. Yet people still buy beer in pubs.
Presumably Quark's business survives the way any other bar or pub does: He provides a gathering place with its own distinct atmosphere.
I seem to remember (but unfortunately don't find a respective quote to back this up) that replicators would refuse to not use Synthehol instead of proper alcohol. And, as that article also states:
Some bartenders like Guinan and Quark, however, keep a supply of genuine alcoholic beverages for customers requesting such.
So aside from the atmosphere some folks wishing to taste real alcohol may not actually have the choice you mention.
Quark's business model seems to rely quite heavily on three main elements; gambling (complete with attractive Dabo girls), real alcohol/ freshly cooked food. On top of that, many of his customers seem to be passing time until their holosuite reservations are ready.
QUARK: I am truly impressed. And I'm not easily impressed. In all my years as proprietor of Quark's Bar, Grill, Gaming House and Holosuite Arcade, I have never seen such a glowing employee performance report.
and
SISKO: We've heard they've been trying to raise capital to rebuild their armies. What are they doing here?
ODO: Sitting. They went straight to Quark's, but not for the gambling and certainly not for the food. They're just sitting.
The Replimat has something of a reputation for long queues, especially at lunchtime. By comparison, Quark's has serving staff to bring food to your table.
BASHIR: And I thought the Replimat lines were bad.
Quark certainly considers the key selling points of his bar to be gambling and the convivial atmosphere.
Come to Quark's!
Quark's is Fun!
Come to Quark's!
Don't walk, run!
Additionally, the Official Star Trek Fact Files #59 suggests that a key selling point is that Quark has a much wider selection of drinks (and presumably food) available to customers than the jury-rigged Cardassian replicators that people have in their quarters.
Quark operates a large replicator unit behind the bar of his establishment, the memory banks of which contain thousands of drinks from all over the Galaxy.
That all being said, you're not wrong. DS9 Writer Ronald D. Moore addressed this (tongue firmly in cheek) in an AOL interview.
Q. Why do people pay for food/drink at Quark's when they can get it for free in their quarters?
RDM: They haven't figured this out yet, so please don't tell them.
There could be differences in the hardware (replicator) or software (replicator program) that could allow it to make more varied/better food.
The evolution in the Trek-verse was:
...and there's always room for improvement.
In The Expanse series (technologically somewhere between now and Trek), there's occasional remarks about the calibration of the food printer being a bit off. The crew on the Enterprise (from Enterprise) are frequently complaining about the resequencers. Even by Voyager with it's fancy computers, ordering a cup of soup is sometimes a hassle.
Starfleet is a post-scarcity society; but that doesn't mean that the Federation, or the Alpha Quadrant at large, is post-scarcity. If it was, there would be almost no business for the Ferengi, and no market for self-sealing stem bolts (or any other commodity).
While we do see replicators in officer's quarters, we don't often see junior quarters, or civilian quarters, except in one episode with Nog and Jake... and their quarters didn't have a replicator. While officers might have the perk to eat in their quarters, most of the people on the station would need to queue for food elsewhere.
Not to mention, one common theme in DS9 was that the Cardassian replicators were not tuned for humans yet; this is above and beyond "replicated food tastes slightly less better" and encroaches into "these flavor proteins are completely built wrong and therefore the flavor is weird." We know for a fact that Quark's replicator has been modded by Quark and Rom over the years. It's also likely that the Replimat uses customized replicators, based on their advertising, to ensure that the "unique" flavors of their food come through.
Replicators use a TON of energy. For Starfleet officers on ships, they just bleed a bit of power from the massive powerplants used for the warp drives and weapon systems; there's power to spare at all times. DS9, however, runs on six fusion generators designed to run a mining platform, and designed to run continuously at 80% efficiency... and actively works against increasing efficiency. They eventually upgrade the power systems for the Dominion War, but for the first three seasons, at least... well, remember, it's a mining outpost, not Earth Spacedock.
Replicators use a TON of processing power, and if there's one thing O'Brien's constantly griping about which isn't the power grid or voles, it's the computer. It's a Cardassian computer, an underpowered one at that, and running non-stop indexing for replicators would likely strain the system. Much easier to build a replicator bay with it's own dedicated offline computer than have a station-spanning network of replicator pads.
Finally, external costs. The replicator doesn't only have to replicate the food, it also has to replicate the plates, napkins, forks, little umbrellas, ice; there's a lot more involved than just replicating "tea." This is where Quark has a leg up: except for the most exotic of orders, he can mix the drinks by hand at the bar, into reusable cups and spoons and mugs. If needed, he can replicate a customized glass (I imagine the British Pub pint mugs Miles and Bashir always used were custom). But in general, because (at the most) he has to replicate a special order (at a higher cost to the customer) or replicate ingredients (simpler forms in bulk)... he can sell his food and drink at a much lower rate than in-suite Replicators can do it... and for beverages probably way cheaper than the Replimat... maybe even at a slight discount to encourage stupider gambling at the Dabo wheel.
There isn't one big reason why Quarks and the Replimat are popular, it's a whole bunch of little ones. For the Federation crew, it's for the camaraderie (I don't imagine Garrick eating lunch at Bashir's quarters every day), holosuite queues, and the general pubbish atmosphere. (It's also possible that they are "encouraged" to "stimulate the economy" with credits and latinum provided to them as part of their compensation for moving to DS9.)
For John and Jane Bajoran and Garrick the Tailor, however, it's simple economics. Their room and board aren't subsidized by Starfleet, so they need inexpensive food, drink, and entertainment. And that means centralized replicators, Quark's bar, the Klingon restaurant, and all the other places to eat on the Promenade.
Quark also serves non-replicated foods and drinks that obviously taste better than that replicated food you can get from any replicator.
