Sports teams move freely from city to city. Movement is subject to the approval of the other team owners (2/3 must approve) and the league commissioner.

A big city without a major sports franchise in no longer truly a big city. If they refuse to "play ball", as it were, the team finds a city that will. The teams do provide a lot of revenue and no cost is considered too great to keep the team, as long as there is a drop of water in the well.

Had it not been for Katrina, this would have happened to New Orleans. The owner wanted to move the Saints to San Antonio and San Antonio was ready to pay. NOLA didn't have the ability to retain the team. After the storm, government pressure kept the team's owner from dealing the city another blow. Since then fed assistance has kicked in to provide the improvements the owner demanded.

Obviously, a football or baseball franchise is of greater value than basketball and so on down the line. You don't see cities in this country kicking in to build soccer stadiums or volleyball arenas.