Generally speaking, a lesson we learned coming out of DPPt is that when you have a meta with much more powerful attacks (higher base stats, higher base power moves than older gens), what matters for STAB is not super effective hits, but neutral hits.
Grass getting hits on a few key types (Water, Ground, Rock), is why I said it makes for a good hidden power / coverage move. As a STAB though? It's pretty bad.
Grass isn't alone in being an attack type more useful for coverage than STAB. Fire falls into this category; without sun and rain messing around with the type-wars, we'd see the vast majority of fire attacks on non-fire pokemon (Dragons, Grass-types like Venusaur/Celebi, etc.). Ice tends to also fall in this category, but that's mostly due to its failings as a defensive type rather than as an offensive one. Still, I think most would prefer to have STAB Draco Meteor than STAB Ice Beam (Neutral > SE on STAB).