The solution is to normalize the outliers by having multiple people. Having 1 person in charge will make a nutcase inevitable one day. Having a 10-person council would require at least 6 nutcases in a single cycle to gain majority, which is very unlikely. And for congresses you up that to ~100 or more.

I also believe you're overestimating competence in current governments. Take any council, any senate, you will see most of them attended the same universities, hung around in the same circles, and so on. Even though you technically have a number of different people, their experience in life overlaps so much you effectively have very few distinct opinions in the room. By randomly selecting applicants you guarantee the greatest diversity of opinions, and thus potential solutions to problems.

Here's what happens when you get 150 randomly selected people in a room and tell them to lower emissions: https://en.wikipedia.org/wiki/Citizens_Convention_for_Climate#Proposals

It is true and I agree that somehow getting the right people in the right positions would be ideal, but the less random a selection process is, the greater the influence that can be exerted over it. I believe the human species would have to fundamentally be different in order to have a more effective selection process than random.