Generally, marketplaces get hooked with very few mainstream payment methods.
Next time there will be a completly new marketplace, with new types of merchants and new market mechanic...you will see a new, major player...but it has to be disruptive to PayPal.
Online to Offline is a new marketplace in many ways...looking for a unified payment. If i am not mistaken, the next big payment player may come from that....
It's an issue when you reach scale, hard to detect, and if you end up being ultra sensitive you end up behaving like jerks freezing accounts for no reason (ie what PayPal does today).
You are also up against regulatory issues (you skirt around becoming a bank = highly regulated) and the massive network effects PayPal/eBay have.
I heard that Square had to pause growth to deal with fraud, and they have the benefit of having Visa/MasterCard/Amex as intermediaries.