This would work in an ideal world. Unfortunately with Presidential positions and even committee positions a certain amount of responsibility goes hand in hand with them, and unfortunately stating that you are speaking as yourself does not under any law I know of absolve you from a conflict of interest.
Different organisations run in different ways.
We need to decide whether the President can act as you have or whether the President should be more of an impartial facilitator and coordinator. If it is the latter then my first comments most certainly apply. The net result of me standing aside will be zero change. The net result might very well be a calmer, different style of discussion. As I have pointed out in a previous post, the discussion under the current moderator has deteriorated to the point where I believe the moderator needs changing.