I don't see a need to ban it because it's fairly unlikely that someone can both afford a Lazy Bear ticket and also be unbanked.
But if you take the nuance out of this question and forced me to choose, then yes, I would say that Lazy Bear should be required to offer a cash-based way to buy tickets.
Your argument is a bit lazy though, right? The point is that cash itself says you have to accept it for "all debts public and private" and as an equitable society we have an incentive to make sure that is true. Out of hand dismissals of a coherent argument do not help us learn more; they only serve to make you feel good about being smarter than some other people.
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.
Restaurants have to accept cash. When you order food you incur a debt. That's what "all debts" on cash means. Buying things in a store is different. No debt is incurred.
Such bans are a cosmetic solution to poverty. They give the illusion of dealing with the problem. But they solve nothing. Prices will be a little higher for all San Franciscans (handling cash, even intermittently, is risky and expensive). Meanwhile, the poor will have no more income or opportunities. But hey, they will have the theoretical ability to buy a plush toy from an Amazon store. (Assuming such stores still make economic sense to deploy.)
Oh, and it's open : M-F, 7:30 a.m. to 5:30 p.m.
One example, FastTrack express lanes in the Bay area (unlike the lanes on bridges, there is no cash-accepting substitute.)
I, too, find it easier to apply consequentialism, but bureaucracies work well when they have clear rules.