You have to consider the interest of the involved parties rather than the efficiency of a system.

Making a purchase is (still) voluntary for the customer.

For everyday purchases at physical stores, cards are convenient. You just swipe and maybe put your PIN. But other digital payment methods or cash can be just as convenient. You're never going to chargeback a coffee, a sandwich, or your groceries.

But for distance purchases such as online shopping, hotel bookings, flight reservations and such, trust is the most important factor, not convenience. Cards have fraud protection. Other payment systems do not. These "unelected and unaccountable" people can actually help you if you've been the victim of wire fraud. Much faster and much less of a hassle than going through the courts. And if they don't help you, you haven't in any way, shape or form abstained from your right to justice through a court of law.

If customers can have that security and ease of mind, then they are much more likely to make a distance purchase. Which means that the vendor can sell their product. If the customer can't have that ease of mind, then the vendor will not make a sale.

So vendors who want to make sales will gladly accept cards. Anybody foolish enough to try to sell without making it easy for the customer to pay in their preferred way will go out of business.

Another point worth mentioning is that cards work instantly across pretty much all currencies in the world. You can go from anywhere to anywhere and pay with your card and currency exchange is done automatically. And in the past 10 years, cards have given very good exchange rates.

> Cards have fraud protection.

This is only in US and it is needed in US, because US has very limited consumer rights regulation. EU has much stronger consumer rights (mandatory 14-day return windows for any reason, easy cancellation for subscriptions, mandatory 2-year warranties).

So the things that the (private) credit-card companies protect you from in US (via chargeback support and fraud detection) are things that laws protect you from in EU.