Should the office of President be non-partisan?

Do you think the government would work better if our Presidents were not allowed to affiliate with a political party? If the office of President were more strictly based on leadership qualities and managerial qualifications rather than policy positions? And we took out some of the policy-making roles of the President such as appointing Supreme Court Justices (and elected them instead)? Do you think a more neutral Executive Branch would make our government work better?