Going by Star Trek History, we have Starships and Starbases as usuable backdrops.
Yes, but instead they would run by "not-Starfleet." Look at DS9, much of the cast was "not-Starfleet." DS9 wasn't a Starfleet space station, it was a Bajorian civilian facility. There were entire episodes where there wasn't a single Starfleet character in sight.
House of Quark (one of my favs) had Starfleet in the background only. They played no significant part.