Yeah, right the king. I forgot about that.
.. Troll-in-training?
No, I was serious about that. Chess with best play is a draw. It isn't that of an disadvantage to have black anymore. In the current world cup there were many black wins out of equal positions because white risked too much too win.
In the suggested variation OP suggested a draw cannot be achieved because even if all pieces are exchanged there will always be a player who reaches the other side first because in chess we alternate between the players.
the king should be allowed to dribble.