We've actually done remote experiments at Stripe in order to do just that. Where whole teams will get spread across as many places as possible and we attempt to keep everything as it was in order to discover the holes in the daily processes we have.
This is why it's a god send if you have a Scottish relative of some sort when you grow up poor in England. A couple of friends of mine used this exact loophole in order to further their education when they had to leave high school.
We almost provide that today with Checkout. If you've used Checkout on a website before, you can easily pay on another site without entering your CC info again.