The entire idea behind credit cards is to force processing fees upon store owners. As a store owner you are required to pay up to 3.5% of your revenue to the processing company (the percentage can be even higher than that if you sell stuff for small amounts, like just a dollar). With cash you can choose your bank and there is more of a free market, while with credit cards you can't get around not accepting certain br…
If the US regulated interchange fees like Europe did (In the EU, interchange fees are capped to 0.3% of the transaction for credit cards and to 0.2% for debit cards, no cap for corporate cards), everyone would still get the benefit of cashless transactions without the processing rake credit card processors and related entities take.
This might be mitigated by the dominant form of payments in the regulated marks you mentioned being debit cards, which in some ways flips the equation on risk around.
However, this might not sit well with consumers. Lots of people in the US like credit cards because of the substantially superior risk profile they present (to the cardholder).