Interesting thoughts, RichardMEL, but since you invited comments, I will say that I am strongly against it. The main reason is self-interest. You say that 'paid F likely doesn't exist, or is at most 1-2 pax per aircraft .' I am not so sure. I know of many people, including myself, who very often fly on paid first RTW (A-class) fares. I cannot say what percentage of the cabin we/they occupy, but I do not think that it is vanishingly small. These tickets are very flexible, and provide penalty-free last minute changes. If UA were to start giving pax double upgrades willy-nilly, or even within a few hours of departure, and potentially depriving paying F- and A-pax of the ability to otherwise walk up to the gate and with very high likelihood get a first-class seat, I would take my business to some other airline in a heartbeat. Also, I have been known to buy walk-up first-class tickets an hour or so before departure due to last-minute business demands.

I have also purchased many cheap coach tickets, and feel perfectly content to fly in business. Likewise, I purchase many business tickets, again many at the last minute, and would be very unhappy if I were unable to secure a first-class upgrade because of a prior double upgrade from econ. IMO, UA had better figure out very quickly how to get more paying business and first-class pax into business and first-class seats if they are to remain solvent.