I don't see someone being shot at from beginning to end. If they got elected, people voted for them, why would they shoot them down before they even got a chance to prove themselves? If their opinion changes later on, then it's because of something they've done that the Writers didn't like, and that makes sense and is a logical balance to the election system.
I say "You can't vote out someone who hasn't been voted in" as application to the normal case rather than the extreme case you're talking about. Most of these types of projects end up at a point where nobody's sitting around HATING the leader. They just wish the leader would do something that they're not doing. If the leader was elected, he is obligated to lead and the people can justifiably press him into doing so. If he just walked in and declared himself project lead, set up a system and began work, and then suddenly had to move to his new apartment and didn't have time to go to forums for a month, there's not much people can do. I've seen that happen where people sit around, not wanting to kick him out but wishing somebody else would for them.
Elections make sure leaders are chosen by merit, as opposed to whoever wanted to speak the loudest. I talk a lot and I probably could grab the reins of the Showcase Age project. But I think people should decide if I'd be a good leader or not. Maybe the Writers feel I'm too passionate and would get too bothered if things weren't going right.