Not knowing the established history of some characters can actually be nice I think. The difference between a blank slate with conveniently made up background and a background that has already been told, in quite some detail, that difference tends to be very noticeable. No matter how "complex" the background made up on the spot is.

When the background has been told elsewhere, it's a legitimate challenge to the unprepared viewer's mind. But when it's made up on the spot, it's an arbitrary riddle. I know some viewers love that kind of stuff (e.g. everybody who made it through Lost I guess?), but to me that just feels annoying. If you want me to apply myself to the riddle, make it part of the story (like in a whodunnit), or don't keep me guessing.

But when it's organically grown background complexity from another story, I'm perfectly fine with it. Patrick Stewart's Gurney Halleck: he just pops up later with atomics, the "how" is not part of the movie adaptation. And neither is speculating about it. It's just an obvious indication that yes, there's more happening in this universe than the part squeezed into anamorphic cinemascope.

That being said, yes, watching TNG after DS9 wouldn't work well at all. It's hard enough watching early episodes after late episodes, because even the "adventure of the week" episodes have been told very differently later, but the universe is too much the same to really disconnect.