Mastercard and Visa are not the only middle-men; the only “payment processors” involved in making sales.
Next time you check out at a cafe, look at the branding of the tablet/software the cashier is using. Chances are, it wasn’t developed by the cafe owners, or by MC/Visa. That’s a payment processor. There’s some big ones out there that can be hard to avoid.
EDIT: While finding exact point of blame remains difficult, a recent statement from Valve suggests I may be wrong about the card companies being innocent, at least with Mastercard. It’s a long chain and it seems each link wants to forward blame.