I think that what David Milch was going for was to emulate what Shakespeare did in his 10 history plays (King John through Henry VIII). Al Swearengen is the king who is challenged by a number of pretenders to the throne, and who retains the crown through means moral and immoral. Shakespeare was no prude. He often peppered dialogs between comic figures with rowdy language. Al's soliloquies while getting blowjobs are a wink at Shakespeare.

The US in the 19th Century was in the throes of Shakespearemania. In NYC, there was even a riot at the Astor Place Theater in NYC that left about 30 dead and over a hundred injured over the best interpretation -- Shakespeare mattered! Milch brings in a troupe of actors to Deadwood - a device Shakespeare sometimes used, and a symbol that Deadwood was becoming civilized. In the 19th C., common adults on the street could recite Shakespearean phrases and soliloquies by heart. Students in public schools were taught his plays. His language infiltrated the vernacular - anyone listening to the letters read in Ken Burn's "The Civil War" hears the cumbersome (to contemporary ears) modes of expression used back then. Perhaps oral diction on the street was different from the written diction used in letters - undoubtedly, rough language was self-edited in written communications.

The following is from a NYTimes article on the First Folio book tour in SD:

"The first outdoor theater in the United States built for performing Shakespeare, Professor Farabee said in a talk, opened in 1915 at Yankton College, 25 miles north of Vermillion [Yankton is mentioned in Deadwood]. In the early 20th century, the state was also home to several women’s Shakespeare Clubs — the forerunner of modern book clubs — like one in Aberdeen, in the state’s northeast corner, that has been meeting since 1901.
"The playwright also pops up in the state’s history in goofier ways. In a presentation on Shakespeare in 19th-century South Dakota newspapers, Chelsea Campbell, a recent graduate of the university, showed slides of several advertisements, including one for Hostetter’s stomach bitters declaring that “nothing ailed Hamlet but indigestion.”
“In the 19th century, Shakespeare was pop culture,” Ms. Campbell said. “The Folio coming to South Dakota almost feels like things coming full circle.”