They are very simple to model and thus well understood. You can easily calculate their error and stability for all possible input, even if you can't model the s

They are very simple to model and thus well understood. You can easily calculate their error and stability for all possible input, even if you can't model the system very well. How do you proof your steps won't create unwanted oscillations for some kinds of input? You can also implement them using very simple circuits or even completely mechanical, but that's probably not too important these days. If you can model the system optimal control is even better. Much more robust than PIDs and can also be done linear using LQ.