One area of cycling where suspension posts are highly beneficial is tandem bicycles. Specifically, at the stoker's (rear cyclist) position.
Stoker has much harder time seeing and predicting bumps in upcoming path when compared to the captain (the forward cyclist). No amount of captain's feedback (oral warnings about upcoming obstacles) can compensate for being unable to directly see road ahead you.
This difference results in much more bumps reaching the stoker's body, leading to higher fatigue and less pleasant ride. Where a captain would instinctively stand up on pedals to soak an upcoming bump, a stoker would get hit in the butt.
Because of this, a suspension post (regardless of its construction) is beneficial to the stoker.
Let's generalize a bit.
Any sort of suspension designed for filtering low-frequency obstacles (such as pot holes, branches, kerbs) is beneficial when you cannot easily avoid them, e.g. in the aforementioned position, or riding trail, riding at night, or steering a low-maneuverable vehicle (cargo bike). Otherwise, it is just easier to avoid obstacles, and it is always safer to avoid them than just to rely on suspension to always save your ass.
High-frequency input (e.g. small irregularities of pavement or gravel) you cannot easily avoid. That is where different kind of suspension comes to play. Traditionally, it is pneumatic tires.