Why would we? A credible threat from quantum computing is decades away. Why would we discuss and settle on a quantum resistant algorithm now, knowing that when it comes to actually be necessary the algorithm we chose today will almost certainly be long outdated and replaced by something stronger, quicker, more efficient, etc?

And as soon as broadcast a transaction from that address, then your public key is exposed, allowing a malicious miner with a quantum computer to steal your coins. So again, if your security relies on keeping your public key private, then your security is broken.

That's absolutely fine if that's what you want to do, and everyone should be avoiding address re-use anyway from a privacy point of view. But it is not a viable solution against quantum attacks.

The old chain doesn't die, we simply introduce a new quantum resistant address type. We've introduced many new address types over the course of bitcoin's history, such as segwit and now taproot, with no effect on previous blocks.

At 200 exahash, it would take the entire bitcoin network about 54 billion years to perform 2¹²⁸ hashes. And that's just simple hashes using highly efficient ASICs. Worth mentioning that if you think 128 bits is insecure, not only should you stop using bitcoin, but you probably need to stop using banks or even the internet and just keep all your money in cash under your mattress.