Wouldn’t it simple revert to the class wealth based system of cleanliness we had before?

The problems you mention here comes from wealth inequality. We still have those problems when wealth inequality exists - people just find other things to differentiate themselves from the poor. I.e. instead of cleanliness, it is wearing the right (read: expensive) brand of clothing. Or owning an expensive car, or an expensive phone or an expensive anything.

Cleanliness used to be an expensive thing so the wealthy used that to show off their wealth. Nowadays, it is other things.

The solution to this problem is not to make things cheaper (again, there will just be other ways to show off status/wealth), but to reduce wealth inequality.