You lost me... What is the difference between an abandoned wallet and a non-abandoned one in this scenario?

Technically, "abandoned wallets" is not something that exists, all you have are "unspent outputs" of transactions. For QC attacks to work the public key to a private key has to be revealed, for modern addresses that only happens when you spend coins, not when you send them somewhere.

I guess some people call early P2PK (pay to public key) addresses "abandoned", but we simply don't know if somebody still controls them.

Interesting. So as long as your wallet has only received Bitcoin, it's untouchable but the moment you transfer any of it, it's at risk of being emptied. The only way to protect any of the funds is to simply move it to another new wallet. We would be in a situation where any wallets (with known keys) can only be sold off in their entirety to prevent theft. However, who is going to want to buy any Bitcoin if the potential buyer's market decreases with each user exiting the market? The inherent value immediately drops to zero because each successive sale would be less than what it was purchased for. Kind of a Schrodinger's wallet, do you really own any Bitcoin if you can never withdraw from it?

The attack when sending a transaction has a time constraints. It will take many any years to go from being able to crack private keys in years/month to doing it in minutes.