Benefits of higher order low pass in a negative feedback loop
Here's one reason: in a real system, some features of the plant such as mechanical resonances of actuators may be present at frequencies above the unity gain frequency defined by the control law, which should not be driven by the feedback. For example, some types of mechanical resonance (e.g. from piezoelectric transducers) have high quality factor, which focus oscillation in narrow frequency bands when energy is provided to drive the oscillation. While with a low pass filter the majority of the plant's deviation from the set point would be suppressed below the controller's unity gain frequency (as defined by the low pass filter in this case), sharp mechanical resonances must not be driven to the extent that they resonate with a magnitude that again crosses the unity gain frequency. In such a case, if the phase at the resonant frequency is close to an odd multiple of 180°, the system can oscillate and become unstable.

A single low pass filter provides suppression above the corner frequency inverse to frequency. Using a higher order low pass filter allows the magnitude of the feedback to be further suppressed at higher frequencies (for a second order filter, by inverse frequency squared, and so on). Higher order low pass filters therefore help to prevent "ringing up" resonant features that can create instabilities.