Earlier quoted context omitted.
I'd love to see what happens if I eat a meal, then say, "Sorry, I only have cash." They can be mad about it, but I don't think I'm breaking any laws by not having their preferred payment method to pay that debt, right? They can even ban me from the restaurant but—for that meal—I can't get charged with theft of services (or whatever the innkeeper laws are that relate to this situation)
Might depend on if there was clear notification before ordering your meal that they don't accept cash. In that case, you've incurred a debt that you knew you would be unable to pay. That might be some sort of fraud but it probably varies by jurisdiction.
"All debts, public or private"