This has always seemed to be like the best aproach. You never want people that gravitate towards positions of authority to be in such positions. For positions that require some degree of competence you have to settle with what you get, but what qualifications do politicians actually have?.

Its not like we have the modern equivalent of the ancient chinese civil servant exam so that civil servants at least have some basic level of competency. Picking at random cannot possibly be any worse than what we have, it would reduce corruption and would create the incentive to invest more in the education of the general public.