5)   Nothing about the Private key is recorded

Isn't the card reader still getting the whole private key, and you are entering it into two forms?

This just seems to solve security regarding the checkout clerk, and asking for more faith placed onto a machine, and the private (closed source) security of the business.

Why not just pay ahead of time, a money-down-payment-to-line-of-credit? Maybe the business could match you 1:1, 2:1 or what have you; for actual money paid into the store, and credit they could extend?

Everyone is on a club savings card of some sort (in the US anyways). Hard to be pseudoanonymous at your neighborly, once-a-week-visting grocery store.