Payment processing is not a free market by any stretch.

Sadly in the US its creditcards or PayPal. Banking system is archaic as hell, no innovation in decades. The big American banks could digitalize and utterly rape PayPal if they wanted but why bother?

what about stripe?

Can I really switch payment processors freely as a consumer? Or is my choice mostly to eat higher prices (^F “cost of doing business” to see my other comment), or not shop using PayPal?

The free market is one aspect of capitalism. The concentration of capital which can be leveraged to undermine the freedom of the market is another.

Isn’t the point of “disruption” so popular in startup culture to leverage the agility of smaller enterprises (and even a pitch used to rise capital) the tool to fight old paradigms? My point being that it isn’t “capitalism” fault, but that the markets are lagging behind the demand and it will fix itself eventually (again, see Stripe efforts in this matter for example).

PayPal is long past the startup phase, though. They're a very well established player, and as such they have power they can leverage. A lot of people feel bound to use PayPal despite disliking the way they operate. That by itself is a sign of the market not doing what it's supposed to do in the ideal case.

Markets certainly don't always automatically fix itself. They require oversight and regulation, or else they tend to result in cartels and monopolies. The free market is great when it works well, but quite often it needs a bit of help.