If we were going to limit profits, we should target visa/MasterCard/amex instead.
They are a true oligopoly taxing the entire economy and have acted in a highly anti-trust fashion. Limiting their fees to something like 0.1% of the transaction is plenty to not lose money and would put back something like 2.8% of every transaction back into lower prices or into the businesses hands.
The actual benefits to consumers/businesses is going to be much less than 2.8%. For one, actual interchange fees today is nowhere near 2.9% like you suggest. It's not a flat rate, and varies wildly depending on the credit card type and merchant category[1]. For instance, a supermarket might get charged around 1.5% if the customer is using a basic credit card, or 2.1% if the customer is using a top end rewards credit card. I suspect that the weighted average of interchange rate across all consumer spending is probably under 2%. Of that 2%, a big part of it is probably also being passed to consumers via cash back/rewards programs. In Europe where interchange fees are capped, their cash back/rewards program are significantly worse than the ones in US. Combining all these factors, I'd say that the total savings to businesses and customers combined is probably under 1%.
I think you're looking at that market from the wrong angle. Competition in the credit card world pushes transaction fees up, because the competition isn't over the fees, it's competition to see who can offer the best credit card rewards. Cash back, airport lounges, travel points, concierge services...
They are a true oligopoly taxing the entire economy and have acted in a highly anti-trust fashion. Limiting their fees to something like 0.1% of the transaction is plenty to not lose money and would put back something like 2.8% of every transaction back into lower prices or into the businesses hands.