While we feel absolutely certain no quillsmith will ever eclipse Britain's Universal Bard as the Everest epitome of what a universal playwright is and ever shall be - and, after less than 400 years of existence, no one can seriously say America has even come close to producing anyone of comparable (let alone equal) stature ala Chekhov, Shaw or Beckett - who'd be [your choice for our Himalayan aspirants?
Arthur Miller ...
Edward Albee ...
Lorraine Hansberry ...
For the sheer poetry, sensitive compassion, emotional beauty and psychological trauma, shattering conflict plus the breadth of his human scope - ours would unequivocably be
My selection of a favorite playwright is Edward Albee.
Hope this thread won't turn into the sort of thread such as Tall Guy's query regarding the greatest American composer. "Great" is typically an uneasy term to define and perhaps we shouldn't limit ourselves as well to only American writers.
Astute point, TeeAre, which is precisely why we've amended the original query.
And the reason we focused specifically on American wordsmiths is the fact our country doesn't have the centuries old inheritance of theatrical tradition Europe does - not that this automatically translates into cultural inferiority of any kind but (ala government, academia and the arts among others) we've still not totally established a transformational tone (or Voice of expression) utterly uninfluenced by the migration of immigrants who are this country's foundation.
Britain, Ireland, France, Germany - to say nothing and everything of the inescapable classical tradition from seminal Greece onwards - have a lineage the U.S. is still attempting to inculcate as its own utterly unique imprint.
We trotted out the individuals above (and there are those you cited of equal merit) whose broad body of work - Mr. Wilson to the specific contrary - falls more in universally applicable line as the worthies noted in the opening paragraph.