The session cookie isn’t a potentially reused human-readable string though. The password is.

If TLS was broken, I would always be able to get your password by just removing the hashing from the login page. I'd also be able to modify all legitimate requests, and be able to obtain your genuine login tokens for any site.

That requires an active attack though. Yes, that’s always possible if TLS is broken, but it takes more work and is detectable. (Not saying it’s easy to detect, but it’s detectable in theory, where passive sniffing is not.)

If TLS is broken, you lose all message authentication, rendering tampering entirely undetectable.

Passive sniffing requires the same attack vector, and the idea of an attacker only utilizing passive attacks makes no sense.

The point is that additional hashing designed for the premise of "broken TLS" fails the thread model test: It is pointless, as the only time it is applicable is when everything is fallen apart.

TLS itself doesn't have to be broken to have an interceptor.

If your machine has TLS being intercepted nothing matters anymore. That would be the equivalent of having a keylogger installed. There's no point in trying to protect such a client anymore, it's game over then.

Passive interception happens. Especially when you're using a cipher that isn't forward-secure; a breach of the server could allow it to decrypt previous sessions.