I always thought cities funded these stadiums to improve their brand, attract investments, jobs ect.
They do.
The promises don't materialize.
Nowadays it looks like Olympics and its ilk (Pam am games) are just fraud by global construction contractors on the masses.
This is why most of the european countries would love to host the olympics, but in a model where it's split over multiple countries. Because hosting it by yourself is purely a prestige project that politicians try to put on their CV.