It absolutely has impact in the cost of the transaction. Even if we forget the fact that US credit card customers are bribed with percentage based cash back, card processors are both providing a form of insurance, and giving both merchants and customers cashflow easing loans. If I pay my credit card in full every time, I am, in practice, paying days later than when the merchant received my payment: I think the issuing bank is dealing with that part, and is not charging the customer for it. Many a transaction processor also ends up paying merchants faster than their bank gives them the money too: Their agreements with the merchants are often a little too friendly, and they have to secure loans for a day or two: There are entire teams out there dedicated to avoiding cash flow problems on the first of the month, when so many subscriptions come in, and a lot of money changes hands.
We also have the insurance component: Say some famous musician and a few influencers decide to launch a new music festival, get a lot of money paid to their festival-making company, and then, due to mismanagement, fail to have a working music festival. Most of the people that paid with credit cards will ask for refunds, and will get them, even if the festival company goes bankrupt. Some of those people managing transactions hold the bag, and end up losing millions in refunds. There's also a wide gamut of fraudulent operations that will try to extract money from the system, either by posing as merchants, or as customers. Some of that fraud is also eaten by the companies that handle the transaction.
So while fees could go down in a world with little fraud (and they do, as companies that are large enough, and have sufficient controls, end up negotiating serious discounts), it makes sense for fees to have a flat base and a percentage base, even if the entire system between you and your customer was just attempting to break even. The right percent though, barring the most fraudulent of environments, has nothing to do with a 30% cut.
The merchants lose when there's fraud/chargebacks, not Visa. Visa forwards that cost to the original merchant. That incentivizes them to be more vigilant about fraud protection, e.g. having to put your zip code in at the gas station.
And the banks that issue the cards are the ones that pay points/get interest, not Visa. Visa simply processes the transactions. If you noticed, your "Visa" card has a bank issuer, like the Capital One Quicksilver card (which uses Visa network)
The cost of running a transaction network has nothing to do with credit card points, insurance, chargebacks. Those are all handled by other parties.
I'm not making a statement on what the right or wrong rate is, but in the case of credit cards there's also a level of risk involved with fraud, which does scale with the size of purchase. Debit cards have less risk and thus have a lower, if not totally fixed-rate, fee.
For chargeback-able transactions and transactions that are reversible due to fraud, it seems intuitive that the expected value of loss would be a function of the size of the transaction.
