I think Herodotus said it best: "A multitude of rulers is not a good thing. Let there be one ruler, one king."
The problem with your idea is that it gets too buearacratic slowing the decision making prcocess. The whole point of the executive branch is to make quick fast emergency descions, thats why the president is given that power and not congress. It is congress's job to be slow, meticulous, and careful in their decision making to make the best descions and not quick ones.