I haven't even remotely read the replies, knowing how the internet works I'm surprised it isn't "America vs British" yet. However, reading the original post. I have opinions:
On one hand, yeah no this isn't a bad idea. It certainly keeps faction owners accountable, something that has been an issue on chaos in the past. I won't name names here. Having a system like this would ensure that the faction is being lead in the way the members want it to be lead. The entire point of factions on chaos is to please the members of said faction, this just ensures they are doing it. If the faction owner is doing a good job, then yes you vote for them.
On the other hand, this is too open to abuse. I've seen systems like this get abused day in and day out. People claim they have the best intentions for the faction they are voted as the leader of, then kick the faction admins and replace them with friends.
I don't like it
Even though I kinda do.