I used to work for the credit card industry like 15 years ago (damn, I feel old now). Back then, you know how much a credit card transaction actually cost (them)? $0.00001 (or something like that). That accounts for all the people they had working for them, the infrastructure, the servers, etc. It'd be even less today.
There's no reason for them to exist. The government should just setup a central bank transfer system with unlimited free transactions already. Or even better: Mandate that banks can't charge fees for transactions. Not to consumers or businesses! They already make enough money to more than make up for it (Source: I work for a bank and transaction fees are nothing but pure profit since there's basically zero cost associated with them).