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And how do I log into my email account to access this one time link?

Edit: Even if it's an account held on a private server, there must be a password, must there not?

Theoretically you could use x.509 certs and a key stored on a smartcard type device, but sure.

Point is, this advice is probably aimed at developers who aren't working on email systems.

Provisioning and maintaining the certificates/keys across even a small user base is a huge pain compared to letting users choose their own passwords.

Hence theoretically. :)