I find it interesting to reason about all of the interesting ways this could still break, as long as the words of Eoin Woods [1] are followed: "Never invent security tech.", to only reason about these things outside of production environments, and use tested solutions there. In that regard, asymemetric cryptography and the frameworks surrounding it seem to be the one way to go.
Of course, that brings up a further question: why aren't certificates the default way to sign up for sites for end users? Instead of coming up with a password, or using API keys or whatever, why not create a certificate through some sort of a browser/external mechanism instead? It feels like no attempts have been made to make something like that easier, so that it'd replace the concept of passwords.
Thanks for your input, but i guess i shouldn't take up too much of your time.
[1] https://speakerdeck.com/eoinwoods/secure-by-design-security-design-principles-for-the-working-architect?slide=31 (or in video form: https://www.youtube.com/watch?v=4qN3JBGd1g8 )