In the early 90s, besides ABC, CBS, Fox, local independent stations, and maybe PBS to a lesser extent, the only other real competition for the kids was Nickelodeon. Disney Channel was still a premium channel at this point, and Cartoon Network was still another year or so away from launching...it really wasn't until the advent of digital cable in the early 2000s that Nick, Disney, and CN were considered on "equal ground".
As far as why NBC's Saturday morning ratings may have been sagging in the early 90s...I think it may have come down to clearance issues among the affiliates. Just compare and contrast the different schedules between NBC affiliates during the 80s into the early 90s--look at which ones cleared the full schedule and which ones elected to air part or most of the Saturday morning lineup, and instead aired either syndicated shows, movies, live (or taped) sports, or news/public affairs in place.
From my own recollections from the various retro schedules here on this site, it did seem like many NBC affiliates did more pre-empting of Saturday morning network lineup than either of their local ABC or CBS counterparts.