Sorry, I didn't see your exclusion of highest offices. At any rate, I do agree with your point that officials should work their way up (in every field for that matter). The problem is that our political system just doesn't work that way for the highest offices which are the most important to us and the rest of the world.
Sure, it would be an inconvenience (even lives can be lost) if our traffic system shut down or the public transportation stops running (although in Boston this is a way of life). However, this is by no means even close to the damage a president or governor can do.