I was curious about this point when discussion came up on HN just recently. I don't see how you could "assign" each non-QR address a new quantum resistant address unless they "claim" it themselves somehow. What can possibly happen to an uneducated mom-and-pop bitcoin holder who never takes up their claim? Someone else who cracks their private key would be in an identical position to them w.r.t authenticating themselves and doing such a claim first - thus it becomes a race

The parent claim is that once quantum cracking becomes real, there would be no more bitcoin in non-QR wallet (because the quants would steal it all).

That's not really what GP was saying, but since you brought it up I think it would actually be insane NOT to - otherwise Bitcoin has an extremely unstable period as 100s of billions of $ worth of locked up BTC becomes instantly fluid the moment the non-QR wallets are crackable.

I.e. it makes sense to have a long term planned migration of what's active rather than any type of instantaneous rush/change.

The protocol isn't what determines how much a coin is worth