We do that, and it's really the point of the portability work. Once every harness's sessions live in one schema, you can manage and search all of them in one place.

The markdown journal is a fair way to do it, and a popular one. It has a couple of limits though.

A journal comes out of a prompt, so it records one way of looking at the session. Whatever that prompt didn't ask about is gone, and you usually find out which detail you needed much later. But the raw session still has it.

Being able to unify the schema lets you do things notes can't. You can continue a teammate's session on your own machine, or pick up a claude.ai conversation in Claude Code or Codex. The new agent gets the transcript: all the decisions in the trajectory, not a summary of it.