For chains where one uses one persistent address, in order to allow other important features, then it could be more of an issue.
Still, I think solutions will probably be put in place before it becomes a real issue.
… hm, come to think of it, the use of public/private key pairs in cryptocurrencies, is, I think, pretty much exclusively used for signing, not for encrypting, right? In that case, it seems like an option based on hashes and ZKSNARKs should be able to play much the same role? So, even if all the purportedly quantum-safe alternatives to RSA and ECC end up vulnerable for the same reasons, I think probably something that only does the signing part should be possible? Or, hm, at least in the interactive setting…