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.