I do want to point out that stadiums in the US are built with parking because of tailgating culture, or more cynically the ability to charge for tailgating culture.
I don't think you understand how the passage of time works. Modern stadiums were built in a world where tailgating culture for sports was already well established.
How much of those parking lots do you think is dedicated to tailgating? (Hint: It's a minor fraction of the overall surface lots).
Tailgating originates out of the lack of nearby bars, restaurants, public spaces around stadiums. That's why there's a trend of newly-built/in-planning stadiums in urban areas with entertainment districts attached. They've realized there's money to be made, and creating walkable spaces just puuumps out the cash.