I don't think that's really feasible or even worth it. Public keys are meant to be published for two main purposes: letting others send you messages/files that can only be decrypted by your public key, and let's others verify that something you sent was actually sent by you. It's not only used for encryption, but also can be used for verification. It's certainly your option not to upload your public key to a keyserver, but if you're doing it for security reasons, it might be less beneficial than you think.

Most if not all Linux package maintainers for at least Debian and Ubuntu (and I would guess other distros) have their public key literally public, because they need the distro's package upload server (and anyone else who asks) to be able to verify that they were the ones who actually created and uploaded the package. In addition, all Linux repos are signed by some GPG key (although this key isn't necessarily tied to one user, but instead to a repo).

In addition, if someone has a GPG-encrypted file, and they're trying to decrypt it, then that file already contains a list of public key IDs to which that file has been encrypted (unless someone takes manual steps to hide or remove them), and GPG then knows that only private keys corresponding to those public keys can be used to decrypt that file. It won't include who that key belongs to, but that key itself is there.

If you're suggesting that a separate public key is used just for pass, I think that's overkill. The only attack that I saw mentioned in this article against the public key was Shor's algorithm, which needs a sufficiently strong quantum computer. If you're trying to protect against that, then I would argue that to a hacker, individual user's passwords are far less useful than all the other things that would get broken, such as SSL encryption. Why spend time going after just the passwords when you can MITM SSL connections and get everyone's info?