I have both an American Express and a Visa (because Amex just isn't accepted some places). The customer service has been nothing but amazing, even when dealing fraudulent charges. And the cards are accepted everywhere.
What I'm saying is, I don't feel any need whatsoever to bypass my credit card company to pass my information off to a start up.
It would definitely be the next step in user lock-in, but you'd start competing with banks and everyone else who offers a way to pay.
Now, I wouldn't complain if they bought some "bypass the credit card companies" service like Dwolla...