Why would they be platonists? Diogenes was the Greek philosopher who shunned material things and famously lived in a barrel. Seems like that would be the ancient Grecian philosopher that might inspire some form of voluntary homelessness.
There's a (apparently un-substantiated[0]) claim that Plato was buff; "Plato" was apparently a nickname and meant "broad" in Classical Greek, referring to his wrestlers physique.
[0] I heard this claim a long time ago, but according to Wikipedia (https://en.wikipedia.org/wiki/Plato#Life) it's apocryphal. The Talk page has a decent argument for it not being the case.
Ah fair, I meant in that they're homeless so they must live in their heads/in ideas which are more real to them (hence Plato), so they're shredded from always being active and outside.