I’ve not met a single person who disagrees with this system.

Well consider me the first.

Then first the plan won't work, those dorms will be run by the very government politicians they are supposed to make miserable. so they won't.

And why must that be a goal in the first place? Instead of improving democracy so that politicians aren't in the pockets of PACs and actually represent the people, you want to just make them both miserable and now unelected.

If you want that random people are in charge instead of politicians a direct democracy system will work far better then this.