There are businesses that specifically don't allow credit cards and only allow Debit and Cash to reduce these fees already and they are still in business. WinCo Foods is the biggest example I know of, so insinuating that it's impossible to operate if you exclude payment method types/cards isn't really true.

Size matters. WinCo is big enough to do that, because it's a chain and a brand, and people make a choice to go there despite knowing ahead of time that's how it works. (That said, the first time I went into a WinCo I abandoned a cart-load of groceries because I had neither a debit card nor enough cash with me.) That doesn't work for a small business, like the ice cream shop in the example GP offered. They will be giving up a significant fraction of their custom.

Of course what parent comment said doesn't apply to 100% of businesses, bud I'd say it does apply to at least 80-90%. So I agree with them that it wouldn't work very effectively.