I get why some communities choose to do it - a sports franchise can pump extra money into the local economy, making the public investment worth the cost. It's heavily situational. Having billionaire owners demand public funding for new stadiums is ridiculous, though - especially if the proposed location of the stadium has no positive impact on the local economy.
For example, Lambeau Field directly effects the local economy - it's a huge boon for Green Bay businesses and the surrounding municipalities. American Family Field - on the other hand - brings very little direct local economic revenue to surrounding businesses as 99% of visitors drive in, park in the designated lot, tailgate, watch the game, then leave all in that rather isolated environment. Virtually no one visiting stops for fuel or food or a hotel room anywhere near the stadium. Both are great environments to catch sporting events, but the environments are very different. Public funding for Lambeau? Definitely. Public funding for AmFam? Yeah, not so much. (And that is actually a rather hot issue right now as our state government is trying to sell the taxpayers on funding AmFam repairs.)