You make good points.
It is a bit of a pain having to verify each note is still good, although arguably one should do this with fiat to avoid forgeries.

I don't know how or if this system can prevent the private key being copied when it is obviously needed to spend the bitcoin in the note in the online on-chain world.
It may be possible to create a situation where the private key is locked into the note and is only accessible by the NFC enabled phone app that allows it to be spent on-chain.