The campy nature is what the franchise was built on, and it is unlikely that the franchise can be successful without it.
The movie that started the franchise wasn't campy. A lot of people seem to be forgetting that.
It wasn't campy, but it
was mediocre. I wouldn't have used that as a template for the series.
Early on, in the Showtime days,
SG-1 didn't seem as campy and shallow as it got later on. In those years, it could have veered more strongly towards being a "serious" show by developing some of its concepts more fully rather than just touching on them and fleeing at anything that smacked of being sticky or controversial.
What if the Goa'uld hadn't been a bunch of comically stupid, shrieking drag queens, but rather someone had made an attempt to develop the notion that they were a "normal" and intelligent, if parasitic, species, which had been made insane by living too many lifetimes/too much sarcophagus use? (Nirrti was the right idea.) What if they had really tackled the tricky dynamics in the Tau'ri/Tok'ra/Jaffa alliance? So much wasted potential.
As for
BSG, I hardly diefy it. Particularly after watching that crappy movie,
The Plan.
BSG is better the less they focus on the dumbass Cylons and their painfully dumbass, botched clusterfrak of a plan.
Stargate is a good premise, executed poorly.
BSG is a poor premise, executed well.
SG-1, despite its shortcomings, was a pretty entertaining show given how "shallow" it was. SGA, on the other hand...
Shallow things can be quite entertaining, there's no contradiction there. I just prefer that entertaining things not be shallow like
SG-1 increasingly got, over its run.