The problem I see with it is that it would take more time to load each game page with loading the extra column, not to mention using a little more server resource with each game played.

Plus as was mentioned, it would "squeeze" the game board since the game notation is there.

If I could, I would recommend an option to also remove the left side column while playing on the game page - which would allow game boards to load a little faster, etc...

If you have a computer, i actually keep 2 BrainKing tabs open, one that has the games I'm playing, the other to read boards and such.