Even so, QCs cannot do preimage attacks on hashes, they can only brute force them faster. For mining, that just means that the difficulty will increase and blocks will stay the same. For addresses, that means that they still cannot find the associated public key because they still can't find the preimage.
It means that the PoW will change from being practically optimization free,
as currently the case with near-optimal ASICs, to becoming extremely optimization prone,
with huge advantages available only to the most advanced and well-funded organizations
(like your favorite 3-letter agency).
That is, mining power will go from fairly decentralized to absolutely centralized.
A post-quantum bitcoin will need to move away from Hashcash to some asymmetric PoW.