You seem to assume that "randomocracy" is a ridiculous idea. Google "sortition." it is difficult to buy outcomes in sortition. Post Citizens United I wouldn't bet against it performing better.
Sortition is (perhaps) fine for things like Congress. For running, say, the FDA? No, I want people who actually know medicine and biology there. For running the Pentagon? I want people with actual military experience there. For running the State Department? I want people who actually know diplomacy and international relations.
No one seriously disagrees with that. The question is whether the State Department should be run by people who showed diplomatic aptitude in kindergarten due to nature/nurture advantages and were thus subsequently groomed for those roles to the exclusion of others.
