The merchant doesn't generally have much choice. I have some friends who ran a restaurant, and they stopped accepting Amex because the fee was too high. They sold the restaurant to an employee and he immediately started accepting Amex again. Too many high spending clients use it and he didn't want to miss out.

Also, even though Costco only accepts a single brand of card (used to be Amex, now Visa), despite their size and market power they accept any Visa card a customer presents.