Why pro-gradation occurs along coastal environments?
If deposition exceeds subsidence, then the water column shallows, the environment becomes more high energy, and so instead of muds and silt, the sediment would be coarser sand and gravel, so coarsening up.

If deposition and subsidence are equal, then the energy of the environment does not change, so similar grain sizes will be found throughout.

If subsidence exceeds deposition, then I'd expect the grain size to ultimately become smaller as the environment becomes more low-energy as the water column deepens. But what you wrote could refer to coarse material being less frequently reworked in such an environment.

Progradation merely refers here to the progression seen, as over time in the sediment size as a basin generally fills with sediments reflecting shallower environments, I think it's typically taught by the progression of sediments seen as a delta progrades into a basin. First with deep water muds, which coarsen upwards as the delta moves into the basin depositing sediment.

So what remains in the layered sediments we see, has a complex relation to the time of deposition, which might be more info than you require.(here's a link to a good diagram, which may help. LInk)