The conventional password system requires you to have a shared password manager on every device or that your reuse or memorize passwords. And that none of the service's users reuse passwords.
I can access my password manager on my trusted device, and manually type in my password for whatever service on any other device. This is exactly what I do for the rare but important time when I need to login on a device I don't want to have total access to everything.
I don't like that for a number of reasons.