Earlier quoted context omitted.
I live in the UK. I am very suprised yes
As European, I find it insane that I could elect the prosecutor or even the police. And in some ways that politicians would have any word on this apart from deciding the funding and laws...
For example, you could decide that a prosecutor is the best at knowing the law, so let's have a law exam where the one with the best score is named prosecutor. However, being a good prosecutor can't always be reduced to a technical know-how. And those good at laws might be those who were able to pay to go to the best universities, buy the textbooks, be allowed to study for years without working, etc. So you also have a bias on wealthy families.
I don't think that the problem of allocation of power in our modern societies is a solved problem...