It's only for hygienic reasons. I don't even want to think about the bacterial conditions inside swimming trunks in a 90° Sauna with a humidity of 90%. I'm surprised about your recommendation as a doctor not to go naked.

I recently visited the Szechenyi bath in Budapest. All guest in the sauna wore clothes and didn't even use a towel. The smell in the sauna room was so bad I left after a few seconds.