I get the impression myself that no singular approach is perfect. They've all been tried and all have flaws. That and different functions of government might actually benefit from different methods.

This is why most practical real world systems tend to be a hybrid of several different designs.

Eg... the US constitution gives us Direct elections (congress) , indirect elections (president via electors, though that has been somewhat undermined), Sortition (juries), lifetime appointment (judges), appointment based on merit (civil service), and probably a few more that I've missed. One can even argue -if one would like to try- that separation of powers counts as anarchistic (certainly it is anti-archon).