That's a lot harder because they have more of a network effect. People have a Visa or MasterCard because it's widely accepted and it's widely accepted because a lot of people have one.
The solution to this is to make it easier for people to get or accept the alternative payment network. Only now you're into regulatory barriers.
The critical feature of PornCard is that you don't have to give your name, right? Except that they're specifically prohibited from offering that.
The regulatory cost of establishing a new card is effectively the same whether you have a hundred users or a billion, so high regulatory costs put a disproportionate disadvantage on small and upstart networks, which would then have to charge higher fees, which would then cause no one to accept them.
The regulations destroy competition and without competition you don't have a free market.