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.
That's true, but there was Starfleet there, they were managing the station. And a majority of the episodes has Starfleet in it. Having a few random episodes with no Starfleet focus is good for getting past the back to back episodes of Starfleet focus. And yes the Bajorans outnumber Starfleet on DS9. But that's just show backdrop. If you look at the senior staff, how many non-starfleet was there compared to actual starfleet.
Jake (He's a odd duck, he's the son of Ben and a civilian)
Main cast is principly Starfleet, and they generally focus around Starfleet issues.