I know the bin is longer than the seat. They keep squeezing more rows of seats inside.

I have seen many different reasons given in different places for the bag charge and did see a lot of cargo along with the bags on my last flight, but why it is pretty irrelevant.

They just do not have enough room in the cabin for all the carryons and they will reach a point where they will need to do something besides gate check carryons. There are many people who feel entitled to that space to have their bags close to them. There are also many people who are more than willing to let their carryon be gate checked for them. There are also people willing to check their bags for $25 dollars, but some airlines are going higher and will probably cause more people to go the carryon route. With baggage going missing or items being lost from checked bags, some are moving to carryons also. What happens when the airline has contracted more cargo on the plane and there are too many carryons for the cabin and there isn't enough space for gate checking or it causes it to be overweight? I was on a flight from Dallas to Branson. It wasn't full of people, but some of the people were support for a music act that was to perform and had a bunch of cargo. The plane was overweight and they bumped 5 passengers off a plane with maybe 50 passengers. I bet that wasn't pleasant for those going for a fun weekend.

Maybe the person's idea earlier about tagging a bag after measuring it would work. They could keep track of how many and know when they would need to start gate checking them and do it earlier before starting the boarding process.

The OP had started this talking about a rude, entitled couple fighting about the overhead space. I just think the airline knows more about the underlying problem that is causing the symptoms that we are encountering on the flights and they should do something to organize it better to avoid having passengers arguing and trying to pull other peoples items out of the compartments to fit theirs in instead.