Why do you think credit card transaction fees exist?
It's to cover fraud/theft with some margin for profit.
Unfortunately transaction fees don't cover the costs for fraud/theft. Basically credit card issuing banks are permitted to charge usury interest rates from people who carry monthly balances (and demographically are generally poor) to make their profit.
The merchants and issuing banks pay transaction fees to the VISA/MC, but the banks charge the interest (and assume the fraud/theft risk).
Just last year, VISA+MC received only $7.8B+$6.1B in worldwide transaction processing fees, but Citibank (one of the largest V/M card issuers ~15%) made a whopping $4B in credit card interest on a loan balance of $146B in the USA and Canada alone.
Note the transaction fees are not only payed to Visa/MC, payment processors (like square) also take a cut of the fees paid by merchants before it even gets to Visa/MC.
(fwiw, Visa also made $6B on currency exchange operations last year which is a profit center for them nearly equivalent to transaction processing fees).
And if you are wondering where them money for "rewards" cards come from, basically it comes directly from the merchants who pay more to payment processors to clear rewards cards than cards without rewards...