Yes, paying a few % on every transaction to move kilobytes of information over a network is absurd. The true cost is less than pennies but the EMV cartel led by VISA has successfully kept the price many orders of magnitude higher, employing anti-competitive tricks like: hiding the cost to consumers by contracually preventing retailers from increasing prices for VISA payments.
Free/cheap digital payments exist (eg. EU SEPA credit transfers); for credit cars, however, the majority part of the cost (and thus price) is not just making the payment but ensuring that payments are reversible in case of fraud and other disputes, and that customers can get their money back even if the money can't be recovered from a fraudster.
If you'd add a reputable escrow service, dispute resolution system and fraud insurance on top of any cryptocurrency, these features will drive the cost up just as high or more.
You are underestimating the cost of maintaining such a network and underwriting the risk of fraud. Before anyone chimes in here with a neckbeard and a “but [libertarian blockchain drivel]” I do not think the effective monopoly that visa has on transactions is a good thing nor do I think it’s the best system.
The funny part is that EC (a German-only card network that stands for the E in EMV, with MasterCard and VISA being the M and V) has less than 0.125% fees for the smaller retailers, and even less for larger ones – you basically only pay the interchange fees.
This is why e.g. ALDI for many years only took EC, but not MasterCard or VISA.
For no reason? You pay visa (or more correctly, the merchant pays) to run a network so you can use your card anywhere, to put time and energy into integrating with merchants and to provide a layer of fraud protection.