where did the OP say they didnt even bother looking??? The OP did say the UC rep said only in a middle seat in Y could be there were no F seats , but maybe all they checked was the next flight out.

Now the OP did say that the supervisor that showed up didnt look but maybe they did look before getting there already briefed why they had to come over. Alot of times I ask for a supervisor anywhere by the time Im transferred the 1st rep brought them up to date, so why not here as well.

I would expect most if ot all of a Mondays flights both LAX-SFO & SFO-LAX to be full up front.

and as some folks posted why didnt the OP simply look to see which Carriers had F space and call NH to FIM them to that carrier

keep in mind the OP never posted hey I checked UA and these flights all showed F seats available , it did seem to me that the OP thought UA should have downgraded anyone who wasnt on a Full F fare and holding a F seat so that they could fly in F, that isnt called for and isnt proper procedure since the OP isnt confirmed on that flight even in Y. Its getting to look like a DYKWIA case