The whole problem with PayPal is exactly that it isn't a bank so they can get away with all kinds of stuff a bank cannot. I doubt a bank backed competitor could

The whole problem with PayPal is exactly that it isn't a bank so they can get away with all kinds of stuff a bank cannot. I doubt a bank backed competitor could survive against a business that can just lock an account with money in it and never pay them back. Not really a level playing field.