Yeah, the Borg are a DQ race, but if they meet the Borg that often they shouldn't meet unassimilated civilizations that often. Any Borg-dominated region of space should be almost exclusively Borg.
It's true, Voyager didn't have story continuity but it did have character development continuity in that they gradually developed characters in a certain trajectory through their behavior in individual episodes, particularly with Seven. But that's not any different than shows like CSI or House have.
Being on the move means they couldn't meet the same people over and over again and deal with the same places over and over again. But they could have established a richer culture aboard the ship, had a strong cast of secondary characters, etc. They used the main cast pretty much exclusively after season two. Any non-main cast crewmembers for the rest of the series who were important in one episode might have showed up and said hi once or twice but basically disappeared. The only exceptions are Naomi and Icheb. Even Sam Wildman basically wasn't a presence in Naomi stories.