Logic and reason have no place in these kinds of discussions. Not many people want to be mayor of Cleveland, but no one wants to be the mayor who let the town's pro team run away.
The root cause of this kind of insanity is the legal monopoly the NFL(and other sports leagues) are granted by law. Football teams are treated more like public utilities. It would be horribly inefficient for a city to have competing power companies, with double power lines strung down each street. It would drive up the costs for each company and in the end be bad for consumers. Fair enough, so we trade enterprise for a regulated market. In the case of pro sports, we don't regulate very much. It seems the pro teams write the regulations, but we are content with that. We hear a lot of moaning about millionaire ball players, but we(the people) created them. If player salaries were dependent on ticket sales, few players would be paid more than $100k a year.
The monopoly makes the television revenues possible, which make some players worth millions a year. This also makes the location of the team almost superfluous. They could be based anywhere. This puts a city in a very weak bargaining position.
