Until such point as all businesses have achieved cashless and there is no choice in the matter left, for anyone. That's the stated endpoint of this game. Why do you think Visa are offering $10k prizes for businesses that can go fully cashless? It's not for the customers.
I would make a point of not supporting such a business but if I'm in a minority and cashless catches on...
Which is why we need legislation to prevent exclusion of significant minorities be they the disabled or poorer people. I'm more than comfortable for businesses that wish to trade on the high street to be required to fit a ramp to their doorway, inductive coils for hearing aids, and required to take cash.
If we end up cashless it will be the poor and elderly who will have the most difficulty. Even now, well over 10 years after the switch, it's reasonably common to see elderly folks in supermarket or bank struggling with chip and PIN.
The thing we're dealing with here isn't Visa, it's the businesses themselves. They've reached a point where dealing with Visa is cheaper than dealing with cash.
I would make a point of not supporting such a business but if I'm in a minority and cashless catches on...