Would you also support a ban on stores that don't accept $100 bills? What about stores that refuse to accept payment only in pennies? The issue is in those cases that $100 bills make them targets for robbery and therefore cause undue burden on those stores. In fact, the same could be said of cash in general over other forms of payment. From what I've heard, China's mostly cashless system is a dream for both consumers and stores.
You make a lot of arguments here, most of which I won't touch (especially saying China is "a dream for both consumers and stores").
But to answer your question: no, we should not have 0 bounds on what is acceptable, and there should be some guardrails to make sure that the pedants in all of us don't take over, and that our economy doesn't end up running on pennies (not that they would, that argument is marginal at best). However, not accepting cash is a problem of a different magnitude than not accepting some annoying forms of cash. I support a ban on cashless stores, but, yes, like you pointed out, with some caveats on what they have to support and what they don't.