With the possible exception of the CRJ-550, there is no narrowbody plane in the fleet that has enough room for each person on the flight to store one regulation-size roll-aboard bag. Even the planes with Space Bins don’t quite have enough space, although they come very close. Therefore, in order to make this work, you’ll need to restrict the size of carry-ons beyond the current published limits — in some cases, significantly beyond. And, since you can’t really run an airline by trying to enforce different bin rules based upon the specific aircraft that gets assigned to a flight, UA would have to use the least-common-denominator on all flights.

Being the airline that forces everyone to check their bags seems like a great way to lose business from anyone who would prefer not to spend an additional 20-30 minutes per itinerary waiting for bags and hoping they haven’t been misrouted.