However just because the mass population doesn't have access to these superior quantum computers doesn't mean its still not a threat. Governments which are probably funding these quantum computers are known to be pretty hostile towards Bitcoin and could use this to their advantage along with other things on their agenda.
I posted why I don't think this will happen
above. In short, governments have bigger fish to fry than 'destroying' bitcoin. If a government were to use a QC to steal a bunch of bitcoins, it would serve as a warning to the rest of the world to upgrade their encryption algorithms that is Quantum resistant. If a country were to have the ability to break EDSCA but doesn't attack bitcoin, it could silently collect/intercept encrypted data/secrets, and learn the secrets being protected by the now broken encryption.
The problem with reusing addresses is once they have broadcast themselves onto the network they are then vulnerable to an attack from a quantum computer because they have exposed their public keys onto the network. This hash would then be suspect to quantum computers by using factoring to break the encryption and this is where I think the network could be improved without implementing a fully quantum resistant ledger by only allowing the use of an address once.
If you were to operate under the assumption that QCs will be used to attack bitcoin, what you describe will only be a temporary solution. Once QCs have enough qubits to calculate the private key within ~an hour, it will be unsafe to spend any coin. The reason is, it is common enough to see hour to 1.5 hour long blocks (the time between blocks) so that someone with a QC could start trying to break the private key of an address 'containing' a lot of coin that was spent within a few minutes from the time the last block was found, and double spend the transaction with a much larger fee once the private key is calculated. The attacker would be unsuccessful when the block time is less than a hour, however a bitcoin user has no way of knowing the time until the next block will be found, so every transaction will be at risk.