But actually they probably do like Quark's shady stuff, because it brings in the sort of intelligence and contacts Starfleet itself would be hard pressed to gather here on the very edge of the UFP sphere of influence. Plus the pettier end of Quark's criminal record is a neat way to blackmail him to doing Starfleet's bidding without actually driving him into such a corner that he would walk away from the deal altogether.
Later on, it also turns out that Quark is a good contact to the Ferengi Alliance in general, and its Grand Nagus in particular, as the Nagus has seen profit in using Quark as his personal front in Gamma Quadrant dealings. Everything indicates that the Ferengi are an important local power, having been longterm business partners with the Cardassians and being very active in forging business ties with civilizations at both ends of the wormhole.
Quark is useful for Starfleet. The business Quark attracts is good for Bajor. And Odo probably greatly enjoys the way Quark attracts and concentrates crime in the neighborhood, making Odo's work all the easier.
Personally, I would have enjoyed the heroes finding and befriending other "uneasy allies" of this sort, in addition to Quark and the invaluable Garak. Perhaps some ruffian from Gamma could have become their streetwise contact to the Quadrant, or possibly a scientific expert to complement Dax? Possibly they could have gained a religious expert from, say, Bareil, to help Sisko out with his Emissary role? How about a Romulan insider, say, the chaperon for the cloaking device? Such opportunities came and went; one or two might have been made more use of.