In doing research on the sustainability of the textile sector, I came across this company that makes a reusable towel dispenser incorporating cloth as opposed to paper. They do business with the big wigs in textiles, most notably Lenzing (makers of TENCEL), so it seems legit.

And if this company does it, I'd wager that others do too.

Imagine if we had this in all countries as opposed to paper towels. Maybe cloth towels + hand dryers for the best of both worlds.

Edit: better link with video showing operation & maintenance.