So if Brady would have gone and attacked the puck, what would the attacking player do??? Umm pass to the guy wide open on the other side forcing the goalie to slide across, now the goalie has to square up to the shot while moving across. Now the guy who gets has the puck is left wide open( because Brady has gone an attacked the guy who is now without the puck-- to either one time the puck, shoot quickly, stick handle around the goalie or deek and then slide the puck past the goalie. The goalie is now left with all these options to contend with in this situation because Brady has taken himself completely out of the play and is defending a guy who is no longer in the play. Furthermore, the goalie had to slide across the net with the pass, thus making him off balance and more vulnerable to any of the options above.
The defender who stays in the middle allows the attacking player to shoot thus creating only one of the options above to be confronted by the goalie who is, if executing correctly, is already square to the puck. Since the defender remains in the center he is essentially defending both players because neither attacking player knows what the defender is going to do and therefore is left with making a risky pass through the defender or shooting the puck on the net. A deek is not an option as the defender is still, again if executing correctly, positioning his stick in a way as to still make possible stick on puck contact which may create a turnover or a separation of the puck from the attackers stick.