My point is that you are taking what should work behind the scenes (common shared secret) and forcing a user interaction (typing or copying out a code) because

My point is that you are taking what should work behind the scenes (common shared secret) and forcing a user interaction (typing or copying out a code) because synchronizing that secret across user accounts on disparate devices is considered "too hard" a problem, even though like I said the browser can be a perfectly good commonality and Persona was on the brink of fantastic innovation on that front.