Point being that if you get a valid TLS connection from a client cert, and then you get another valid connection from the same cert tomorrow, you can be very certain that the entity connecting is either the same software environment that connected earlier, or an attacker that has compromised it. You can be cryptographically certain that it is not an attacker that hasn't effected a full compromise of your client.

And there's value there, if you're a server. It's why XMPP wants federated servers to authenticate themselves with certificates in the first place.