Well Minato is Hokage but his talent and jutsu is best used for battle to win the war. The Third steps in for the war because of his knowledge. Minato isn't in the right position to lead a war it was best to let the one with experience handle that job. While The third took the job temp. for Minato(And also Minato was by the 3rd's side to gain knowledge too), he used that time to train his team or for them to train themselves. All of this was before the war maybe from once they first began and until days before they enter war.