What kind of crap gets upvoted here nowadays?
You seem to have forgotten all the other things credit cards do. Like giving you a credit. The cost of debt DOES scale by the amount. Or did you expect to have a mortgage with a "flat interest fee" because the cost of transacting loan doesn't scale with the size of the loan?
Not to mention credit cards have you covered in case of fraud and your card gets hit with transactions. If they're fradulent, they just get cancelled. You're not out of pocket a single dollar. But if your cash gets stolen, or your debit card gets used to drain your account? Yeah good luck. (Debit cards have improved in this sense, but will be a longer fight with your bank compared to credit.
What else? Insurance/consumer coverage for items you buy. The cost of that ALSO scales with the purchase. An expensive TV is expensive to replace on the credit card insurance.
Unless you pay a specific credit card fee or there's a cash rebate, you're best off paying with the credit card since the price is the same. But with the credit card you get the perks (see above), with cash or debit the merchant just takes your money. Let me repeat: if you don't use a credit card, you're still paying the same amount!
But that's not to say things can't improve:
The EU put in place a cap on the fee allowed at 0.3% for CC, 0.2% for debit. And we still have all of the things above. And some rare 1% cashback cards.
But to say that it doesn't make sense for the fee to scale with the amount just because the cost of the transaction is the same is just silly.