>a PID controller, which is a form of control that only really looks at error
As the name implies the PID controller relies on proportional, integral and derivative information about the error. What you mean is a purely P controller, which just relies on the error.
Missiles are also not guided by a PID controller, that would be silly. They (or the guidance computer in the airplane) has to take into account the trajectory of the target and guide the missile in a way to intercept that target, which is not something you can accomplish with just a PID controller.
As the name implies the PID controller relies on proportional, integral and derivative information about the error. What you mean is a purely P controller, which just relies on the error.
Missiles are also not guided by a PID controller, that would be silly. They (or the guidance computer in the airplane) has to take into account the trajectory of the target and guide the missile in a way to intercept that target, which is not something you can accomplish with just a PID controller.