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).
I disagree. Just the fact that Grass hits Water, Ground, and Rock super-effectively makes it a better STAB to have than Steel. This is because the types that Steel hits super-effectively are very rare and it is also resisted by a lot of Pokémon. However, what is true is that Grass will never get perfect coverage when paired with anything (assuming that you are using just two attacks) because no matter which type you pair with Grass, there is always a type that wall both attacks. So, you paired Grass with Ice? You are walled by Fire-types and Steel-types. You paired with Fire? No longer walled by Steels, but now you have problems with Dragon-types and didn't solved your problem with Fire-types. Rock hits super-effectively every type that threathens Grass (except Poison), including Fire, but good luck trying to get past Steel-types. However, the combination of Grass-, Poison-, and Fire-type attacks has surprisingly fantastic coverage (it only misses out Heatran). Yes, I am speaking of Venusaur's STABs combined with HP Fire.