I think you are talking about the real public restrooms. I produce hand soap, hand sanitizer, and household cleaning
supplies, I assure you they are used. Public restrooms are a problem. People do carry their own toilet paper, it's how it is, we all adapt. People who use public restrooms also carry individual hand wipes in their purses. And hand sanitizer.
There is still a lot of 3rd world issues for 2/3 of the country, and maybe you travel in those regions. But after LIVING in China for 20 years and having traveled in every province for work except Qinghai and Tibet, I think I have a pretty good finger on the pulse.