Why do you think SSH-Keys are safe against phishing? I mean it is unlikely, that someone will just send the key per mail or upload it somewhere since most ppl using SSH-Keys are more knowledgeable.
When you now get an easy one click solution to transfer Passkeys from one Cloud provider to another it will get easier to trick a user to do that. Scenario: You get a mail from Microsoft that there is a thread and that you need to transfer your keys to their cloud.
How would you sync or transfer a passkey across devices without transferring the private key?