I think that Star Trek can indeed be looked at as simply a space opera in space, but its basic premise--that of a diverse crew out among the stars--also allows it to be allegorical at times as well as tackle moral issues. But Trek is also an action-adventure series, so it can have big explosions, space battles, and fight sequences too.
In a real sense, Trek is not one single thing. It can be thought-provoking and silly; character-driven and non-stop action; seriously dramatic and unapologetically campy. As such, it appeals to an incredibly wide audience: people of different ages, races, creeds, nationalities, etc. Both an ivy-league college professor and a high school dropout can find something
about Trek they like, even if they're totally different things.