Just think, somebody's naked butt would get wiped on that cloth ten times per day. That's a deal-breaker right there.
Actually naturists have a strict towel policy. (Not unlike hitchhikers.) You always have your towel to sit on. Problem solved just by enforcing a "graphic side down" towel sitting policy.
You can not get anything worthwhile done without raising a sweat. -- The First Law Of Thermodynamics