[zymhan]

How could you programmatically create a credit card without some pre-existing financial relationship with a a credit card issuer?

There's a good reason you cannot simply create and destroy payment cards without any trusted third party keeping track. Money laundering is the obvious issue.

[PeterisP]

Well, you'd presumable have some pre-existing financial relationship, all the legal agreements and stuff; it's just that instead of (or inaddition to) having a "long-term" credit card number you'd cycle through a bunch of disposable short-term credit card numbers. I.e. your relationship with the card issuer is long-term but the instrument you use to interact with merchants is intentionally limited to a short term.