Well, one of the big issues is there are only a couple networks that you can run CC transactions through. Visa is being sued by the Fed for monopoly. They make it so if you want to get the best price, you need to reach thresholds of total charges. Which forces vendors to use their network for all transactions to get the best price, rather than using others if their immediate pricing is lower.
Discover is another network which may be purchasrd by Capital One. They are waiting on approval from the Fed, but may not get it since.it would give one bank control over one of the few networks left.
If they could make it so the networks were more competitive, it would likely lower fees for merchants but there are no guarantees. Often, companies will raise prices to match competitor pricing, as they all want to charge more rather than less.