But if they made it clear at the time of ordering that they didn’t accept cash, then a customer who orders knowing that’s the only payment medium they have would presumably be the one breaching the contract when they weren’t able to pay? I guess the remedy to that would be to create a debt, but I’d also presume that could also include any other damages incurred by the coffee vendor for facilitating the cash payment.

The debt doesn't vanish, you've just transferred it back to the company. They aren't making coffee without cost.