In the early 2000s (EU) I was in a high school and a sports team, both very white, and this was already a thing… We didn’t take showers after gym class, and we didn’t take showers after sports, which annoyed my dad to no end as he drove a car full of smelly teenagers back when we were the visiting team.
For me it makes much more sense to link it to a visual culture where the nude body is sexualised, together with the cultural hegemony of the prudish USA. Nipplegate was in 2004, and whereas nowhere in Europe you’ll find quite as hysterical reactions to nudity, these attitudes did get exported to an extent.