TOTP is also just hashing a password with a time salt. The purpose is just to prove that you are in possession of the device that stores the password without actually ever entering the password anywhere where it can be leaked. In this case the device is just your brain.
And that makes it a password (i.e. the primary factor, not a second factor). The whole point of a second factor is that it's not trivially cloneable (hence why, for example, SMS is a poor form of 2FA in the presence of widespread SIM cloning attacks).
No, the defining characteristic of a password is also how it is used: it is communicated in the clear to the verifier, thus revealing it to eavesdroppers. It is highly non-trivial to clone the knowledge in someone's brain if they never openly communicate the mTOTP secret but only do the computations in their head.
> No, the defining characteristic of a password is also how it is used: it is communicated in the clear to the verifier
This is only true if the verifier lives on your local terminal - otherwise we use an encrypted channel to transmit to the verifier, or do the exactly same type of timed-salted-hash scheme used here to transmit without revealing the password.
Not true. There are lots of authentication schemes where the plaintext password is never communicated. This becomes rather crucial when the client doesn't know for sure yet what the identity of the other side is. See for example wifi encryption.
Cloning the knowledge in someone's brain is fairly easy. You just need a wrench.
Yes, but that is not how passwords work since the protocol for proving knowledge is that you enter it into the HTML form served by the party claiming to be the verifier.
If we are talking rubber-hose cryptography then a physical hardware token is just an insecure as a brain. Most people are not hacked via wrenches.
In other words: it's how passwords work on websites. Because it's usually good enough, as the only thing you are protecting is access to the server on the other side, and the pipe to that is already encrypted with TLS.
But this isn't a hard requirement. See Protonmail as a counterexample. And again, wifi authentication. I reckon debit card PINs as well.