All true but it misses one of the most important points, as these discussions almost always do.  The case for Shakespeare is not just that he teaches edifying life lessons, has timeless psychological insights or that he is part of a common cultural capital.  It is mainly that he makes wonderfully inventive and virtuosic use of the English language.  Jesting at scars, star crossed lovers, sweet sorrow, a rose by any other name, and a hundred other happy examples come to mind immediately.