Granted, quite a few politicians would simply burst under the strain. I think we could afford the loss.
Think of the salutary effect when the survivors realize that the world won't end if they can't get their oar in. And that things don't get radically worse when they are obeying other people rather than having other people obey them.(**)
The higher the office, the longer the stay required.
(*) Yes, I know Trappists don't actually vow silence. Close enough, though.
(**)Some politicians are capable of learning.