It's funny how so many non-Americans call our payments system "backwards", but I generally prefer it to bank-transfer-based payments:
1. When I pay with a credit card, I haven't actually spent any money. That money is still in my bank account, and I have the chance to dispute the transaction if it's fraudulent, without putting my own money on the line first. I've heard a few horror stories where a merchant/service has mis-charged a debit card or ACH transfer, and the time it took to get the money back caused stress around things like making rent payments. It frankly doesn't matter to me how common or uncommon such a thing is; it's literally impossible when paying for a credit card. (Yes, I do have to trust that the credit card issuer themselves won't make an error when debiting my bank account when the bill is due, but I prefer only having to trust one party not to make mistakes, than some larger number.)
2. While everyone is of course paying for this through higher prices in stores, I'm reasonably savvy about using credit cards that give me cash back or rewards points or something, and tailoring what card I use to benefit a particular transaction (for example, one card might give 3% back on grocery purchases, while another might give me 3x points on travel expenses). Ultimately I end up paying a bit less for everything than if I were to use cash or a debit card (or a bank transfer). Certainly some merchants have credit card surcharges, or discounts for paying cash/debit, but I find that those are a tiny percentage of my transactions, and I can always use cash or debit in those instances. It's hard to say how much (if at all) prices would actually be lower if credit cards (and their associated fees) didn't exist; handling cash isn't free either for businesses (counting/reconciliation, storage areas, security for transport to a bank, etc.).
The main issue with our useless bank-transfer payments system is person-to-person payments. But these days, with Venmo, Cash App, and Zelle, that issue rarely comes up (and all of these are free for the sender if you use bank debit rather than a credit card). I can't remember the last time I had to give money to a friend that involved using cash. The big downside of all of these (similar to cash, I guess) is that there's very little fraud protection. If you send someone money, and they screw you over, you might not have much recourse.
I very much consider our banking system backwards in many ways, but I find our payments system to be just fine, and, in some ways, quite good. And our banking system is backwards in part due to lack of demand.