Man has to stand for 7 hour flight due to fatty next to him.

[Low C Sharp]

If we were really paying for the space we use, people with larger carry-ons would pay more than people carrying, say, a purse only.

I don't agree. That just means that both a purse and a rollaboard fit within the airline's first weight/space category. On my airline, extra baggage is priced in 20-pound increments, so 50- and 69-pound bags pay the same surcharge, and 70-pound bags pay a larger surcharge. Grouping usage into categories rather than measuring it by the milligram is still charging by space/weight.

"What we're paying for is transportation from point a to point b."

No, we're paying for the transportation under agreed terms and conditions. Irrespective of FAA rules, an airline would be breaking their contract with you if they made you stand during the flight instead of giving you your own seat. Imagine that your neighbor put his feet in your lap and told you that it's fine because you both paid to get from point A to point B, and you'll both get there. Would that be OK? Heck no -- not with the airline, and I'm sure not with you. He agreed to certain terms when he bought the ticket. He's entitled to X, not Y, during the course of the transportation, and you can find out just what X is if you read the fine print.