The value credit cards add over cash is not just convenience at the point of sale. I favor using my credit card because it's easier to track my expenses when every transaction is itemized. I would never have the patience to keep receipts for every cash transaction and tally them at the end of each month. Having this control over my finances saves me money in the long run, because I'm not making stupid spending decisions that will force me to borrow money later.

The real problem with credit card companies isn't the transaction fees, it's the high interest rates, late fees, etc. If they only give cards to people who pay their balance each month, they go bankrupt tomorrow.

The transaction fees are indeed higher than they'd be an open and competitive market without network effects, anticompetitive behavior, etc. but if you want to start breaking their stranglehold on the consumer, you need to do what the CFPB has done and hit them on the obscene late fees, confusing language in the agreements, and deceptive marketing practices. Focusing on trying to keep down transaction fees arguably attacks the one legitimate purpose they serve, and would force them to try to get more money from penalty interest and late fees on customers who are probably already in financial trouble.