.... This system requires that the majority work according to the protocol in any case.
...
The NY vending machine can only take the coin if it controls a lot of CPU power and can generate a block, but the whole bitcoin system is built on the assumption that the vast majority of CPU power is honest. And being honest with my proposal means following the pseudocode above.
Right, that's my issue with your proposal: what incentive does the NY vending machine have to be honest? It can be "dishonest", ignore verifiers all-together, and accept more transactions (better for it) with less work (also better for it)....
The NY vending machine can only take the coin if it controls a lot of CPU power and can generate a block, but the whole bitcoin system is built on the assumption that the vast majority of CPU power is honest. And being honest with my proposal means following the pseudocode above.