Cryptocurrencies would be the last thing I worry about w.r.t Quantum crypto attacks. Everything would be broken. Think banks, brokerage accounts, email, text messages - everything.
https://radar.cloudflare.com/adoption-and-usage
In contrast, cryptocurrencies have to upgrade the entire network all at once or it’s effectively a painful fork. That effort appears to just be getting talked about now, without even starting to discuss timing:
Bitcoin is much more centralized than the popular imagination would have you believe, both in terms of the small number of controlling interests behind the majority of the transaction capacity, and just as importantly the shared open source software running those nodes. Moreover, the economic incentives for the switch are strongly, perhaps even perfectly, aligned among the vast majority of node operators. Bitcoin is already dangerously close to, if not beyond, the possibility of a successful Byzantine attack; it just doesn't happen precisely because of the incentive alignment--if you're that large, you don't want to undermine trust in the network, and you're an easy target for civil punishment.
Stragglers are a problem, of course, but that's why I thought this would be a harder problem for Bitcoin: for me to use PQC for HTTPS, only my browser and the server need to support it and past connections don't matter, whereas for a blockchain you need to upgrade the entire network to support it for new transactions _and_ have some kind of data migration for all of the existing data. I don't think that's insurmountable – Bitcoin is rather famously not as decentralized as the marketing would have you believe — but it seems like a harder level of coordination.
In fairness, the original Bitcoin white paper referenced both (1) distributed compute and (2) the self-defeating nature of a Byzantine attack as the means of protection. It's not as though (2) is just lucky happenstance.
Hence, why proof of stake can exist.