I don't think the staff did it, it sure seems like it came from network higher ups, and their ridiculous notions of what would and wouldn't sell, what was and wasn't trendy, etc.
Also the network was the one insisting on immediately going into production on ENT the second VOY was wrapped. No one else wanted that, not B&B, in the S2 docs even Scott Bakula says he tried to use his clout to tell the network to wait a while before starting ENT, to no avail. So they ended up pushing ENT through in the same year and burning everyone out.
It sure sounds like the UPN/Paramount execs who watched Trek be a consistent cash cow throughout the '90s just couldn't see that it was being pushed too much. They just wanted another show using the same previously successful formula.
Something that Gene Roddenberry was able to side-step by going the syndication route with TNG (and DS9), there was no network pushing him. Trek then being tied to a network (a mediocre one at that), UPN, really seems like a large portion of the undoing/oversaturation.
In the Season 2 BD docs, one of the S1/S2 writing staff (Mike Sussman I think, can't remember now it's been over a week since I watched it) interviewed, says something like "we didn't set out to make a bad show".
Braga and Berman both take some responsibility too. Braga still seems to take things very personally. He admits that he should have fought for a proper prequel more, when the network wanted more of the same (i.e. VOY style), instead he acquiesced and freely admits he shoehorned in the temporal cold war stuff to appease them.
Berman also very briefly says perhaps he stuck a little to staunchly too his "What would Gene do?" mantra.