Hereabouts and any place I've been in China there's a grand tradition of wetting your hands after visiting the (stinking, befouled, unkempt) bathroom. Students line up to douse their hands and then wander away arms akimbo and hands flapping. I've seen (broken) hot air blowers in train stations and soap and paper towels in airports but that's luxury. The healing, broad spectrum anti-bacteria powers of air and water are enough for the masses.
Unrelated perhaps, although awkward juxtaposed now, is what I have never seen. That I can recall, I have never seen a Chinese lick their fingers. Long ago I read somewhere that as part of politeness, you don't draw attention to your mouth. As a girl, cover it if you laugh. As anyone else, keep your fingers outta there. It's something I'm aware of every time I eat an apple in public. I will of course attempt, once the apple is mostly consumed, to render my fingers less sticky. No one falls over themselves to stop me, nor do people recoil in any particular horror, but I have the sense that me licking my fingers is privately scandalizing all within eyeshot.
Carpet however has nothing to do with this. My issue with carpet is other people should own it. Living in close and closer proximity to unrelated neighbours requires a finesse that this society isn't developing fast enough.