>The idea is that the secret key material is never compromised as it is assumed in all security cases.
That's not true, we have (perfect) forward secrecy, backwards secrecy and key rotation mechanisms because we often care what happened after the key is inevitably compromised. In this case the problem makes it hard to "rotate" the keys in a meaningful way, but I'm yet to see a proof it's impossible.
I think we are talking about different things here or the conversation is not clear.
The assertion you mentioned is the "what" assumption while what you said is the "how" we came to that assertion. Most probably you take my word idea in a specific sense other than I wanted to use. My answer was informal because we are here in HN and not writing a paper.
That's not true, we have (perfect) forward secrecy, backwards secrecy and key rotation mechanisms because we often care what happened after the key is inevitably compromised. In this case the problem makes it hard to "rotate" the keys in a meaningful way, but I'm yet to see a proof it's impossible.