Not only that, but how are they supposed to go about doing it?
Fans would crap themselves if Liberty took some of the budget and 'invested' into the community.
If you moved a baseball team to Atlanta, you wouldn't put it where Turner Field currently is. They took the location because they got the stadium for free. This is their chance to go where they want to go, so they're taking it.
If you're upset with someone for them leaving the city, it should overwhelmingly be the city itself, not the team.
It's not really that foreign of a concept; you scratch my back, I scratch yours. The City of Atlanta agrees to relax some form of taxation or zoning or revenue sharing and in turn the Braves make an 'investment' into the community by the way of a dual-use facility or a restaurant or simply expanding/rehabbing some of the areas around the stadium. Both parties benefit.
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I don't think Cobb is even necessarily where the Braves 'want to go' -- it just so happens that the county's taxpayers were duped into paying for an extortionately high percentage of the new stadium and the team was given a sweetheart deal (full control of all revenue streams, free land, etc.) that some teams (St. Louis/Miami/Oakland) looked for/have been looking for for a very long time. In that sense, the move was a no-brainer. But in many other respects it is almost woeful.