But who chooses the best people for the role? Are people voting on all the candidates or is there an elected administrator? If there is an elected administrator, how can we be sure they don't just pick their cousin or someone who bribes them?
Who decides on the actual solutions for the items of importance? How are budgets divided up, who approves that?
A political party doesn't just set overall policy, they do a lot of the administration as well. If there are agencies involved, they'll report into the political party's administrators to work on the detail. This is why I don't think this could work... the level of decision-making required is almost infinite - the public doesn't know enough to make those decisions.