not a bad suggestion. The important thing is to filter between general chat vs self note or hidden team chat. When the chat is very active, it's hard to find the note between the noise.

To improve the game chat why not put two game chat. At left the game chat as we know now and at right the chat for "note to myself" and the hiden chat for team playing. That will allow to keep the note that we use in the game instead of being lost in the reply of the general chat.