Actually it doesn't matter how much you pay for a ticket. The airline writes the rules and can toss you off for any reason. Your ticket is just a promise to transport you if its convenient for them.
As a practical matter, it does. Every domestic airline with which I'm familiar prioritizes involuntary bumps by fare paid. First class, business class, full coach, etc., will not get bumped off the flight (thought they may get downgraded) before cut-rate nonrefundables. If you don't want to be bumped off a flight, pony up for the more expensive ticket up front.
So while the airline has the legal right to do this, from a business perspective ALL U.S. airlines have a serious PR issue.
And yet, air passenger travel generally increases every year. Why is that?
People want to have their cake and eat it too. They want cut-rate fares, but want to lug massive "carry-on" bags on to flight, they want their snacks, no bumping, etc... Just look at the bottom lines -- U.S. airlines are not huge profit machines over extended periods, and a lot of them struggle. It is a very, very competitive industry, and finding the right balance of price/service is not easy.