The reason this is a dumb idea is because coordination and timing. When does the cutover happen? Who decides which transactions no longer count as they were "broken" b/c of quantum computing? The idea is broken but not from technical fundamentals.
As for verification being expensive, it sounds like you don't know the actual costs. It's basically a hash. Finding the pre-image of a hash is very expensive to the point of being impossible. Verifying a pre-image + hash function = a hash is extremely cheap. That's the whole point of 1-way functions. Bitcoin itself is at ~1000 EH/s (exahashes per second)
Again, this isn't a technical problem. It's a coordination problem.
This whole scheme fails if an attacker can manage to delay a transaction for a day, and if the commitment also commits to a particular transaction fee, then the user trying to rescue their funds can’t easily offer a larger transaction fee if their transaction is delayed. But if the commitment does not commit to a transaction fee, then an attacker could force the transaction fee to increase arbitrarily.
Maybe the right strategy would be commit, separately, to multiple different choices of transaction fee.
...probably some people would be very inconvenienced by this. But not as inconvenienced as having the coins stolen or declared forever inaccessible.
I don't know why anyone f's around with crypto anymore. So many caveats, such a scammy ecosystem. It just doesn't seem worth the trouble to support a ransomware and money laundering tool.