The issue seems to be that GA's are eager to gate check bags before boarding. But, once you are onboard, FA's don't seem to want to have people swim upstream with their bag to leave it at the cabin door. It really does become a logistical nightmare at just the time when people need to settle in so that aircraft can push.
I would far prefer that FA's notified the FA at the cabin door when the OH is just about full and the cabin door FA did a hard stop at that point. No more bags. Period. Life goes on if the aircraft goes out with one spot in the OH empty. But, I've been on countless flights where we've pushed late because the final bags need to be stowed in the hold and the kabuki dance between ramp crew, flight deck & dispatcher to get the correct bag #'s for W&B gets delayed.
Needless to say, none of this would be an issue if the carriers enforced their own carry-on policies. While not every aircraft can acommodate a roll-a-board from every pax, not every pax has one. Forcing the gate check equally throughout boarding would likely mean that the last pax on has the same opportunity to carry-on as the first.