Compromising the main keys isn't enough, need to compromise each session key as well in turn, a massive increase.
Forward secrecy addresses this specific attack:
* Someone builds a archive of your encrypted messages, possibly without your knowledge or consent.
* That someone then gets access to your secret key material.
* They can then decrypt their archive.
The session keys are exchanged by the asymmetrical systems that the imagined quantum computer would be able to break. So the attacker gets the session keys directly. So for, say, signal, they only have to break a new key exchange which doesn't happen all that often. They can just run the hash ratchet after that. Even for TLS that does a new session key per connection, that connection might last a fair time. The 10 min can be spread over multiple connections for this proposal. We are hardly talking about a massive increase of difficulty.
