Why could Hamlet be considered a problem play?

He was the hero if this piece. With pilot's eyes: eyes that miss nothing. He had to fulfill his father's wish and avenge his father's death, in doing so, he died for what he believed in. And he rightfully avenged his father's death by killing Claudius while he himself had little time to live. He was important because the play was based off revenge and the troubles of anger towards a person. He loved and he lost. He lived and he died. And even though the tragedy between Ophelia and Hamlet was that Ophelia died before Hamlet had the chance to tell her his true feelings, Hamlet did tell it to everyone before her grave "I loved Ophelia. Forty thousand brothers could not, with all their quantity of love, make up my sum."