Fungibility in Bitcoin Cash

[Windowly]

It seems Dr. Craig Wright has a way up his sleeve to provide pretty amazing fungibility to Bitcoin Cash. He's mentioned it in a few of his lectures this year.

This is from his lecture in Zurich.

Another little thing we can do is re-share private keys, without it having to be on a block.. . . we’re not centralized. Which means we don’t need Lightning. Because if I give you a share, and I can provably remove the share, and make that share invalid using a zero knowledge proof, you now have control of the key, provably. And it hasn’t happened on block. . . We are going to release ways of doing off-block transfers that are instantaneous and that are peer.

https://youtu.be/URajERvVFf4?t=1h3m40s

If there can be instantaneous off-block transfers -- mixing can also be done off-block and and it would seem then all chain analysis is broken. (Particularly if this is done a lot. There will be no assurance that a particular private key is always in the possession of just one person.)

Does anyone have ideas of what other implications would result from these kinds of peer-to-peer, instantaneous and private off-block transfers?