Eliot van Buskirk of Wired suggests that the answer is no, at least for now:
The two main reasons for this are the big players’ massive network-effect advantages, and that the internet cannot match the reliability, speed and security afforded by credit card company’s private networks, according to MacPherson.
“People tend to underestimate the network effect: A payment system is exponentially more valuable the more people participate in it,” said MacPherson, adding that competing with Visa and MasterCard is nearly impossible, “unless you can find a niche that the card companies are not serving, like PayPal did with eBay. Even PayPal, now, is usually just a conduit for a card or a checking account.”
The truly excellent post goes on to explain that the main advantage of Visa and Mastercard is that they’ve invested heavily in building secure private networks that are hardened against hackers and identity thieves. This might ease the sting of Visa and Mastercard’s monopoly rents, but only slightly. Most of all, it is a testament to the enduring power of old-fashioned investments infrastructure, and the power of path dependence, even in app-driven economy.