I've actually had a few runins in my past with some US senators where I got to actually sit and listen and converse about some problems. I was always unimpressed with the caliber of the man, to be honest, in terms of both their emotional and cognitive prowess. Having random people vote on the issues probably wouldn't yield worse results.

Something I've come to believe is that US democracy doesn't naturally select for anyone based on leadership skills, credentials, or any virtue that is needed in such a role. It seems to select for people who can get votes, which can mean a lot of things. I think that is a key issue.

Despite what the law says, people in the administration don't actually have to follow the orders of their appointed superior. If they feel that the senator/congressman/president/etc can be fooled, or simply that enough of their colleagues are on their side, they can just ignore even direct orders. What's the senator going to do? Call the police because their subordinates are ignoring them?

So one of the most necessary qualities in an official is being able to control the levers of power - through connections, charisma, physical power in ages past, money - whatever it is, you need your subordinates to actually do what you tell them. Government isn't a boardgames where people follow the law just because those are the rules of the game.

Me neither, but it reminds me of the Arthur C. Clarke novel "Songs from Distant Earth". In it, a distant colony of Earth has a very small population, since the planet is all a big ocean, except for a few small islands. The small society has a mayor, who's randomly chosen from the population for a limited term. The only disqualification (other than obvious things like age) is that the post can't go to someone who actually wants to do the job. It's similar to how no one in their right mind actually wants to sit on a jury, but people do it because of civic duty.