Indeed. Olympic hockey is a perfect example of a step in that direction, and one of the greatest versions of the game in existence.
If it ditched the requirement that the game always be played on ice, the skill level of hockey in the US could be comparable to its basketball. All those high school football stadiums could get some asphalt surface, chainlink fencing to stand in for the glass, and a few sets of sticks and inline skates, and we could all watch hockey on Friday nights instead of kids knocking their skulls together.
Even shirling (snake baiting) would be better. No-fly Quidditch would be better. Robot fighting league would be better. Two old barbershop guys telling shaggy dog stories would be better. A magnified view of an ant colony devouring a moth would be better. Just watching the grass on the field grow would be... worse. There is a line.
Football is fundamentally flawed. Many positions exist entirely because it's rough and violent. Players who never touch the football in a well played game.