The ease would be in not having to sign up in the first place. Place your order, put in your phone number, answer yes and you're done. Smaller sites would be the winners.

You could also more easily implement time-delayed transactions. Make to order-deliveries sometimes don't charge up front, but instead opt to charge when they're about to deliver. If you (the seller) could send a simple SMS asking for payment, or phone a number when you (the buyer) got the invoice instead of having to sign in with your bank on your computer it'd make life easier for at least some people.