If you're middle class or higher, a credit card is a no-brainer in the US. I pay for 1 international trip a year + a few domestic trips just using my card for every day purchases. I rack up points, pay everything off, and benefit tremendously.
Every great once in a while I will run into a small business that doesn't take credit cards, or offers a discount for cash. But it's quite rare.
In the US, I'm sure people would scream and cry if the evil government tried to take their 2% rewards, even if it meant 3.5% lower prices. We don't like math very much over here -- as this thread is proving.
The merchant costs for processing the purchase of those products is baked into price though. The net effect is that the fees the merchant pays push your retail price up. You're not really getting a benefit if you get 2% back and the retail price is 2% higher to account for the merchants processing fees.
In the end, aside from the complicated consumer reward part, the amount that the credit card companies get isn't that different from the European system.
But the customer pays the merchant. It's all paid by the customer.
However actual businesses have overhead for dealing with physical cash as well. It is slower at the teller, needs to be manually counted and recounted, transported (sometimes with security) and so on. It is not clear whether real costs of handling money are greater or less than merchant fees.
Until that happens, I'll take the 5% cash back, since it is preferable to 0% cash back while paying the same price.
Which, coincidentally, is the benchmark for "decent" credit card rewards.
Some cards will offer rewards on certain kinds of purchases, often up to 5%, but offering only 1%, or nothing for other purposes.
Since the average person only has a single credit card, the majority of cardholders produce more in interchange fees than they collect in rewards.
There's also some complicated accounting voodoo that I don't truly understand, that effectively means that banks can treat extended credit as a pseudo asset, plus, whenever alone is outstanding, it's value is added to the virtual money supply.
It is possible for an individual customer to get significantly more in rewards than interchange, but as this is a relatively small portion of customers, most issuers do not seem to care.