The 2.9% + 30cents on every transaction
There's the flaw in this idea.
The merchant's bank collects 2.9% + 30 cents (in this example). A portion of this is transferred to the issuing bank.
The amount transferred is called the Interchange Fee, and it is significantly lower than that amount. There are different fees depending on the card type, credit/debit, rewards, business cards, etc.. and they are set by Visa/MasterCard/etc. Discover and Amex have more latitude here, since they are both the issuing and acquiring bank... but if they raise fees too high, merchants will just stop accepting their cards.
Interest from the card balance is kept by the issuing bank.
So you see, revenue from credit cards is divided between multiple parties...