When is a controller in automatic not able to do anything to reduce an oscillation? When will a controller amplify an oscillation? In both of these cases, the controller is doing more harm than good by wearing out valves and upsetting other loops.
If there were no unmeasured disturbances, feedback control would not be necessary. Process engineers and operators could home in on the best PID output and just leave it at this value. In fact many process engineers are much more comfortable with setting a stream flow per a process flow diagram...
Much of the differences in approaches to controller algorithms and tuning can be traced back to assumptions made about the type and importance of disturbances. Each method has merits based on the disturbance frequency, location, and time lag.
Fast oscillations are particularly insidious because the best thing a PID controller can do is ignore them. Action taken by PID controller can do more harm than good in terms of resonance, amplification, and perpetuation leading to increased process variability and premature valve failure.