England/the UK and the US retained close connections during those 300 years; it isn't as if we split and never spoke again.
And my black grandfather used to say that Country Music is the white man's Blues.
So, ought American high school musical programs focus exclusively on country music and I don't know... classical music but ignore Blues, Jazz, Rap, House Music, Pop and so on?
I've read some Shakespeare. What has it done for me? I've read at least two books by Iceberg Slim too. His famous autobiography
Pimp: The Story of My Life had at least as much dramatic impact on me that Shakespeare. Truth be told... Iceberg's book educated me more about
my America than anything from Shakespeare. And Shakespeare was no where near as racist or anti-Catholic as say... almost a centuries worth of Southern Jim Crow in the USA.
Shakespeare has been viewed as possibly Catholic in an era of Catholic persecution in England. The conception of vengeance being more ruthless and pronounced by murdering a before he has a chance to confess his sins is culturally and doctrinally in keeping with a Catholic orientation of life in this world and after death.
The United States--even its Catholicism--is often more influenced by Calvinism.
But the USA is the size of a continent. England can be fitted into the State of California and certain aspects of American culture can shift across state and regional lines. The French and Spanish have left as dramatic--if not more--an influence on Louisiana. And I should include the Amerindians, Black-American slaves and free class Creoles, and even the Haitians that fled from Haiti during what was far more a monumental revolution (in Haiti) than that patrician revolt against the Crown of England called "The American Revolution" (which would not have succeeded without the help of the French, Spanish, and the black and mulatto Cuban soldiers under the Spanish Crown.)
To understand certain aspects of Chicago and Milwaukee life on the black streets, it is more enlightening to read Iceberg Slim than Shakespeare.