Sport does bring a lot of misery, health issues and violence too. Fans fighting, wrecking down whole cities, trains. The amount of health issues caused by sport is high if not extremely high.
You forgot to mention that plus the fact sportsmen are rarely sportive.

It's not many people only that might cause infections but the need to find out more about the virus and how it will mutate too.
It's clear it's in body fluids, spit, blood, sperm so probably in sweat too.

In my country sportclubs, sauna, etc will not start before September 1st and if you ask me it is a goid thing plus it will save the society a lot of money.

By the way there's no need to get fat if you eat healthy, delete carbohydrates out of your food and excersice at home. Even muscle contractions laying in bed or sitting, while walking, can give you a better body shape.

Good luck and stay safe.