Absolutely agree and its been on my list since RFIII. Will definitely be implementing this one in EA.
For a long time I've held off simply due to the thinking that "the need for a chat log implies the game isn't giving enough information on screen". But pretty much everything your saying is true in terms of acting like a learning and analysis tool to help gain a deeper understanding of the game.
I think having it hidden by default, and having the option to have it minimized and then expand when you mouse over (as well as an option to keep it up all the time) is a great solution. It sort of puts it in its proper place as: here's a useful thing you can totally look at when somethings not clear, but its not a thing you really need to pay attention to normally.