Why have suspension stems disappeared? I remember in the early 1990s contemplating getting a suspension stem for my 1989 non-suspended Rockhopper MTB. 



I'm surprised that suspension stems appear to have essentially disappeared. Why? They seemed a cheap and easy solution to give a bike front suspension. They could also be made lighter than suspension forks. What were the negatives?
To make suspension effective, it must decouple light-weight moving parts from heavy stable parts. For this reason it is most effective to suspend the wheels - they will move fast up and down, while the frame and the rider will not move vertically. A suspension stem is not very effective because it does not carry much vertical load. A suspension seat post is better but will never work as well as wheel suspension.

You can observe the same principle in cars: light-weight aluminium rims are better for suspension than heavier steel rims.

In sort: suspension stems are ineffective for suspension, add weight and complexity, and potentially dangerous failure modes.