If OP travels frequently but not quite enough to have airline elite status, wouldn't it be in the best interest of OP to just sign up for a United credit card and get Group 2 boarding and not have to deal with bag check at the gate? This is not going to change what happened to OP's recent flight nor the injustice OP feels about having to force check the carry on.
However for people without any UA status (or status with any other airline when flying those airline), there will always be an issue of which group they will board with and if there are enough space in the overhead bins when they board.
If you fly only a few times a year and are mainly a leisure traveler, the credit card is not really necessary and the extra 30 minutes at the baggage carousel isn't typically a big deal on the larger scale. But for business travelers and time-sensitive meetings, boarding early by just having an affiliate credit card may easily be justified and may even able to write off the annual fee as a business expense. I am not pushing for credit cards in any way, but I know they are big profit centers for the airlines and they tend to push people in this direction. Perhaps indirectly forcing more passengers to bag check at the gate helps their credit card sign-up business...