I think the point is that you have a better idea of what you want it to remember and even a small hint can have big impact.

Just saying "write up what you know", with no other clues, should not perform any better than generic compaction.

You should do your own experiment when you see compaction about to start use the end of your window to have it write one first, and then let the session compact and compare. I was surprised by how small the compact message is.

When I tell it to write a letter to itself I usually phrase it.

'write a letter to yourself Make notes of any gotchas or any quirks that you learned and make sure to note them down.'

It does get those into the letter but if you check compaction a lot of it is gone.