Since 1990 municipal and state governments have devoted a positively embarrassing amount of money to publicly financing sports stadiums in the United States. The first of the new wave – Comiskey / US Cellular Field in Chicago – in 1991 is now one of the oldest stadiums in Major League Baseball (only Dodgers Stadium, Fenway Park, and Wrigley Field are older). It is also a rare example of a stadium built with borrowed funds (the State of Illinois did a bond issue) that were actually – hold your breath – paid back by the team. As far as public stadium deals go, that's about as good as it's going to get. Most of them are so much worse, and the new Atlanta Braves stadium swindle is perhaps the worst yet.
Almost every publicly financed stadium is approved by local governments (and sometimes, but not always, by referendum or ballot measure) based on the twin fallacies of promises of massive economic benefits and zero tax increases for local residents. The economic benefits tend to be either short-term (the city hosts one Super Bowl, and then what?), accrued entirely to a handful of people (team owners, concessionaires, and whoever got the parking rights), or greatly exaggerated (turns out that demand to buy expensive tickets to see a mediocre or bad team is insufficient to fill a stadium). As for the zero tax impact argument, it depends on a very specific and, shockingly, deceptive definition of that concept.
Municipal budgets are close to a zero sum game. There are ways to generate new revenue but they are politically unpopular and tend to be measures of last resort for elected officials. So, in the Braves current situation, it is true that the county is not raising taxes to pay for the stadium. What they will have to do is raise taxes to pay for everything else in the budget that they can no longer afford since they devoted all of their resources to the stadium. It's like someone blowing their entire paycheck on the casino and then asking to borrow rent money; the lender isn't really paying the rent, it's paying the person's gambling habit that precludes them from paying their own rent.
No matter how many times this trick is played, local governments seem to keep falling for it because WOO SPORTS! and a dozen local real estate and construction companies stand to benefit tremendously from the arrangement. Those same business interests tend to have a loud voice in government at the state, county, and municipal level. The fact that Cobb County had to monkey with the rules to prevent the public from having any input on the stadium decision suggests that voters have begun to figure out what a boondoggle these deals are. The fact that the public was not allowed to vote or have input suggests that the people behind the deal knew, or strongly suspected, that voters would never willingly swallow the costs involved. We might learn our lessons slowly, incompletely, and at times incorrectly, but there are enough examples in the last two decades to convince even the most enthusiastic sports fan to think twice before supporting free handouts to help people who are already obscenely rich make even more money.