If the fixed costs are not in the transaction fees, then how are you proposing that those are funded? Connectivity fees that penalise low volume stores?
The fee often isn't a percentage. It's sometimes a fixed fee, sometimes a fixed minimum with percentage beyond that. There may be upper limits in place.
It should cost more to process a $10,000 purchase than a $1.59 stick of gun.
Yes, it should. Higher loss in the event of fraud, and a $1.59 purchase usually isn't even going to get checked against card balances, to keep the network traffic down.
Interchange fees are however an interesting thing, and very easily misunderstood. I worked for a corporation that had a retail arm and a card issuing bank. They proposed using cards issued by the bank to pay all of their supplier invoices, so that they'd get the interchange fees back.
No thought about the cost to the bank of providing that service, the card payment fees owed to VISA/Mastercard, the suppliers tacking on card surcharges or the cost of money impacts of using a credit card (although they could have used non-credit payment cards, they also wanted the interest free period from using credit card).