The baseline price for payment processing is well below 2-3%. In the EU, credit card processing fees are capped at 0.3%, and these companies are still able to make a decent profit despite.

What those high fees really come from is the need to cover the cost of all those rewards programs that are so ubiquitous in some countries such as the USA. Those would probably disappear pretty quickly in the presence of a law allowing merchants to add any processing fees (perhaps above some nominal baseline cost) on to the bill. 1% cash back doesn't seem like nearly so great a deal when you have to reckon with the fact that what's really going on is that you pay 2% more, and then the issuing bank gives half of it back to you, along with a generous dose of smoke up the ass, and then pockets the other half.