I looked into it and the currently leading proposal: Hourglass v2 is pretty clever. Once 'Hourglass' is enabled, the rate at which legacy (P2PK) coins can be spent is (proposed to be) capped at 1btc / block. Thus they will not be burned, but the rate at which they can be stolen/compromised will be limited such that the economic impact is at most about 1/3 the block reward.

This gives holders of those old addresses the maximum amount of time to move their coins to more modern addresses and still the ability to move some coins after the deadline. If legacy keys are compromised in bulk, IE access to sufficiently powerful quantum computing is rapid and widespread, then there will be high competition via the existing txn fee bidding process for that 1btc/block slot. Thus most of the value of the will be captured by the txn fee and go to the miners, effectively boosting the mining reward by ~1/3.