Sports teams actually do a good job of bringing a city together and generating lots of ancillary small business (aka jobs). This is why they get to suck at public trough so much.
Please don't ask for links on this -- I haven't been able to find them. That being said, I remember when Los Angeles was looking into a team (the team went to Houston and cost that lovely city $2 billion in public funds) the NFL (and LA Board member Mark Ridley-Thomas) tried to convince us that teams generate revenue, but there were several definitive studies that demonstrated that it is a net loss and, at best a break-even proposition.
That's why we don't have a team. Every now and then LA can show collective intelligence.