> Each chat is its own SharePoint, so it is really simple to lose documentation through things getting siloed.

That's a feature not a bug.

Chats are for quick collaboration on documents. You share it, you get immediate collaborative editing, you do what you have to do and then you eventually archive the document somewhere it makes sense to archive it which in MS Teams would be a Team.

I really like the break down between Team which persists and chat for one off things but I know it really throws off some people.