Comment by lilyball

Besides the fact that stiffness shows up as a term in the equations, stiffness is a concept that can be demonstrated via analogy with a rubber sheet, and so lends itself to a somewhat more intuitive understanding.

Also, the math section demonstrated how stiffness produces both the short-range effect and the massive particles, so instead of just handwaving "massive particles is somehow related to the short range" the stiffness provides a clear answer as to why that's the case.