The actual economics of this never really check out. They never, ever really equal out unless it's a truly transformative event like Bridgestone Arena in Nashville, or in other words an entirely new team & sport to a city. When you're just moving across the street, the city and state are getting money stolen by someone so rich they could pay for the stadium twice.
Especially in an NFL situation where all an owner has to do is tell a lender they own an NFL team with guaranteed hundreds of millions in pure profit a year.
I think the economics vary with the sport.
I don't think football works at all. The big parking lots used for very few dates does not work. I infinitely prefer the model Bob Kraft ended up taking, with some limited infrastucture improvements, private capital for the stadium, and the opportunity for Kraft to grab any synergy by owning and developing the surrounding land. He gets to use the lots for Patriot Place when the Pats aren't playing. he bought the land himself. It's not like Angelos asking the state to buy the land for him so he can make money. Frankly, do that, he should get no money for the stadium since he profits off the development.
I do think both Nats Park and the Gallery Place arena (MCI/Verizon/Cap 1) probably catalyzed some of the development. Whether it was going to happen regardless is another question. Largo ended up finding an alternate use, so the Arena in particular was a good thing. I think if you have a baseball park or both hockey and hoops in an arena, at least the facility is used 80+ nights per year. I think a two team arena is a bit better an investment than a baseball park just because there can be more concerts and other uses like college sports.