There is a little bit of misunderstanding from your side which I think Charles-Tim was trying to point out. If you followed up with the few threads that has been discussed probably in the technical board or elsewhere, you will notice that a major vulnerability being talked about is always the public key. The public key has been viewed as the vulnerability in deriving a private key, and I believe you know what the private key can do when it gets in the wrong hands.

So, the cold wallet is literally like another medium of storage, because the majority of uses a hot wallet. Ideally, Public keys are not visible in this new forms of wallets(Segwit) because they are only shown in their hashed form. And according to what has been said from the quantum point of view, the actual public key can then be revealed if a transaction is made from that particular address.

Let me give an example.
Let's assume this is the hashed form of the your public key - (f5d8fe39a430901c91b02bef5f4c1a5dc74252). This is what everyone should see on the Blockchain. But the moment you make a transaction, it then reveals your real public key, which we all believe can be vulnerable in deriving ones private key.