This could lead to Bitcoin losing public trust - creating a lose-lose situation for both society and the Bitcoin community as a whole.
And how is freezing those coins anyhow different? In both cases, people lose access to their coins. This, also, undermines trustworthiness. Imagine going into your wallet after 5 years and realizing your transaction is invalid, because bitcoin "upgraded" to rules that consider your coins "too dangerous" for the network to have them vulnerable.
This phase is designed to preserve trust in Bitcoin by ensuring that users don't permanently lose access to their funds.
And what about paper wallets? Or bitcoin wallets that weren't generated using some HD standard? Or timelocked coins? Or any coin sitting on a public key?
Freezing coins provides no benefit to the network, as a whole. Only potentially to bitcoin holders, as the supply of money declines. If coins are not frozen, then there's a time period during which a quantum attacker might be able to recover many of them. This will result in victim holders losing access to their coins, and non-victim holders losing purchasing power. If they do get frozen, victim holders still lose access to their coins, and non-victim holders might not lose purchasing power. The only difference is that in the latter, pro-freezing scenario, we make sure that every single victim holder, with coins sitting in quantum-unsafe addresses, will certainly lose access to their coins long before a quantum attacker appears; we are precautionarily violating their property, which is something deeply against the philosophy of bitcoin, in my opinion.