Why have a PID controller for a DC servo motor?
If you are considering a complete servo mechanism which moves to the angle you tell it (eg. an RC hobby servo) then you don't need a PID loop because it already has one built in. In normal operation the servo's internal PID should prevent overshoot.

However, if you are controlling a system which might need varying servo positions to avoid overshoot or maintain stability, then you need an external PID loop. In this situation you could use an open-loop servo mechanism which is just a motor and feedback sensor.