I don't see how it any less dangerous than drafting a psychopath who finds that they love killing in the military? Given the same lengths of term and a new draft to fill all positions in each cycle, no single politician would be in power long enough to garner enough political power to be powerfully dangerous. It would also make it pretty much mandatory for every to receive a competent education because anyone could end up in any position and would need the ability to be competent in that work. It would also complicate lobbying as large companies would have no idea who to groom or pay money to in order to gain influence. It would also get rid of the need for party politics.

I don't see a downside that is any worse than the status quo.

@redbai Re. Military draft, I completely agree. But I also don't support a draft system, and we have not had a draft since Vietnam. Selective services registration at this point is going through the motions. The military brass WANTS volunteers over draftees. Why? Competence. It is too inefficient to have to keep training new replacements for these high tech positions the modern military depends on. Government arguably is similarly vulnerable. Political Congressional aids are indespensible as it is. They are sometimes the only ones keeping ceryain Congressional reps afloat.
Re. Government competence and civics education, I can't picture some people ever being competent, regardless their education. I also have difficulty trusting that said necessary education would be provided broadly, sad to say.
But I still agree there is nothing about the current system to ensure competence, and we certainly have some alarming domestic terrorist-sympathizing, science-denying, theocracy-promoting yahoos in now who clearly don't beling in government.
I don't have the answers, but the one thing we know about elected officials now is that they volunteered and so presumably are motivated. Maybe if we can eliminate the motivation of shameless corporate lobbyist money, some of the "swamp" element that discourages other competent would-be public servants from seeking office could be reduced.