This may be an oversight, or intentional.
It seems as if grass blocks have been left out of the #lush_plants_replaceable tag that controls which blocks moss can spread to. This seems like an oversight to me as Grass, Dirt and Flowers are all part of this tag.
Affects:
Grass Blocks
Coarse Dirt
Podzol
Mycelium
Dirt Path
Rooted Dirt
Farmland
Can confirm.