Even the Pentagon has restaurants in it. All the people who work there are going to want some civilian entertainment.
The Ferengi currency is gold pressed latinum... is is pretty much the US dollar of Star Trek as every other culture but the Federation uses currency.
And you pretty much said it. Ships from all over the place are coming and going, so they're all going to want shore leave and the Promenade is basically one big mall for all the civilians.
You don't expect Starfleet to provide a place to drink, gamble or have sex in holodecks do you?
And Odo... well he's a bit of a fascist at times... he'll regularly detain Quark without due cause, never gives him a lawyer, wants to break up unions and peaceful protesters because they're disorderly and things like that. I like him but he does have a ironfisted streak in him.