Maybe it would be based on cryptocurrency, or a more traditional form of currency that is centralized but isn't USD, for instance. Or someone with a lot of money decides that having dominance over a new economy takes the opportunity and forms their own "competitor" to Visa, but it operates within the economy that Visa decides it doesn't want to be a part of. Then again, maybe Visa one day leaks enough customers that it decides it's not worth being as moralistic.
Bank transfer?
If your customers start to expect to pay using some cryptocurrency, what do you need credit cards for?
First you have to reach a critical mass for the alternative payment system, but the more legitimate businesses that PayPal boots to the other side of the wall, the more mass there is on the other side of the wall.
Also, it's even not so much PayPal as Visa and MasterCard, and how they got the way they are involves both politics and backroom dealings.