Yeah, as someone who grew up in a VERY right wing household (and has made the transition to a much more liberal point of view), it kills me seeing the left make the same ~~logical fallacies~~ bad arguments to fear monger against the right as the right would use against the left.
Edit: probably over thinking my own wording. Its probably not a logical fallacy to assume your enemy is united, its just an inaccurate argument. Changed comment to maybe better reflect that.
I really like that notion.
I think the reason it wouldn't work (at least as you've described) is the myriad of sub-governments (and therefore smaller elections) that can exist for each voter.
My city does town council elections, my county does its board of supervisor elections, plus an occasional county ordinance vote, plus state elections and ballot initiatives, and then our federal president and congress elections all on the same ballot. If I move to a new city, up to half of the relevant people to vote for could change - probably closer to 3/4 if I moved states.