Well, as a business owner, I do have some idea of who "really pays" as you put it. When I charge my customers with Credit Card, I get charged a CC fee (around 2.9%). It's not that there is a free lunch anywhere: the merchants pay for it, as well as some consumers who pay interest on their balances, and some consumers who want special features from their CC.
But as a consumer myself, leaving debt part of the equation aside (since it is irrelevant to the transaction itself), I pay zero transaction fees with my CC, whereas I'd have to pay a significant fee with a cryptocurrency.
More annoying is that the cryptocurrency fee would be charged every time I make a payment. Looking at my CC statement, I can see I & wife made about 50 CC transactions last month, which would result in a significant "monthly fee" if we had used Bitcoin for example (to pick the most "widely adopted" cryptocurrency).
Like I mentioned above, cryptocurrency has very specific key positive aspects, but low transaction fees aren't one of them.