The cheap, older 'analogue' servos were just PI, but the new 'digital' servos have much more advanced control. They actively reverse power to the motor when get

The cheap, older 'analogue' servos were just PI, but the new 'digital' servos have much more advanced control. They actively reverse power to the motor when getting close to the target to extract regen power from the motor inertia while still getting a faster response. Yes, you can get this from PID, but you can't keep it at full reverse right up to the moment it hits the target without getting nasty oscillations as the voltage changes.