No taxpayer ever does and yet every time there's a new stadium built, the taxpayers and the pain. Every time.
You won't get to have a say in it so to me it's a moot point.
True story: When I lived in Minneapolis I worked on a successful campaign to amend the city charter to say they couldn't give more than $1 million for a new privately owned stadium unless they first passed a public referendum.
The Metrodome was literally collapsing and they did need a place to play but that wasn't the point. The point was whether the residents of the city would have any say in how much of a new stadium they would be paying for.
When Wilf threatened to move the Vikings the state legislature simply over-road the city charter (with the support of the mayor, who had been officially for the charter amendment when she ran for office). Ultimately the state, county, and city paid for something like half of the ~$1billion US Bank Stadium. (I believe that figure doesn't include infrastructure improvements).
No politician wants to have to run against an opponent who blames them for "losing" the town's beloved team. Some of them may try to fight for a better deal but sooner or later most of them will cave in, and the owners will never have to contribute enough to make it hurt. In the mean time other projects, for example repairing crumbling highways, will have to wait.
One question I always had was why do fans favor a bigger stadium with crappier sight lines "so Chicago can get a superbowl" instead of a smaller stadium where you can actually see the game from your seat without having to watch it on the jumbo-tron? Do you feel like it personally gives you more prestige?