As long as online payment institutions remain unregulated, then their idea of 'banking' is a joke. I find the possibility of online payment systems taking over in their current form highly unlikely, and frankly, downright laughable.
Literally every single person I know has been burned by paypal in one form or another. Whether being forced to wait as paypal decided to hold funds for an indeterminate amount of time, to having their accounts frozen and loosing funds forever. As long as that remains the status quo, paypal (and other systems like it) will remain a novelty. It is far easier to scam someone out of funds using paypal than it is to rob people at gunpoint, and it's more anonymous too.
Personally, I think paypal is a haven for crime, with the institution itself being the largest culprit, but that is just me.