Author here! I think that warp specialization is inherently related to multi-stage pipelining, they aren't really alternatives of each other. Warp specialization is a way to realize a multi-stage pipeline in the face of hazards that may cause the pipeline to spill out of the register file or not let parts of the pipeline run concurrently as desired.

The fact that we tend to need different warp specialization strategies for different hardware is a consequence of the capabilities of that hardware (i.e. different asynchronous instruction types), and contributes to the complexity of targeting that new hardware.