I agree that the next session wants conclusions, not the whole transcript. What I've seen working with people on this is that a summary only has what the summarizer prompt asked for, and what they need from an old session changes depending on what they're doing when they go back to it. With the full session still around, they can just ask it again.
Porting is also cheap, since it's just a format conversion. Getting a new session back up to speed from notes usually isn't.
Concurrent sessions is a separate problem, and I agree that a message is the right shape there. Where portability helps is that different harnesses are good at different things, so you can start a task in one and move it to another that's better at the next part, without starting over.
As for the summary, I agree that it's a big gap. I'm not trying to make a better summary: it's not a separate summarizer rewriting the session afterwards, it's the session itself writing while it's still active.
"Asking the old one again" works as long as it's alive. In my case it's exactly the opposite — either I've hit the limit, or I've switched to a different model. Then there's no one to ask, and whatever wasn't recorded is gone.
And "cheap" is measured from the wrong side. The conversion is cheap, but the transcript doesn't go into a file — it goes into a live session and spends its turn every time it moves.