Shakespeare wrote for the masses. Competition to attract a paying audience was fierce. The theater had to vie with other entertainment options including the horrifying bear-baiting bloodsport down the street.
The cheap seats were standing room only. The action on stage had better be enough to keep these groundlings' minds off their aching feet and instead on the characters in the play.
The terrible brutalities of human nature held their own against contrived animal fights. The Elizabethan era seamlessly accepted bloodthirsty ancient Roman themes as its onstage entertainment.
Shakespeare is not an elite literary tradition reserved for the educated. It is for everyone who breathes and feels and lives. Human nature is human nature. Some emotions are universal. Love, trust, betrayal, protectiveness, tradition, ritual, sacrifice, celebration.... it's all there. "Titus" and "Much Ado" are two of the more accessible plays, in my opinion.
Come to think of it, "Fiddler on the Roof" is pretty good, too.