I suppose though that the whole thing is that he didn’t have to be all those things. He began well but lost his way. As such he fits Aristotle’s definition of a tragic hero from “Poetics,” in which a tragic hero was defined as one who falls from grace into a state of extreme unhappiness, not by being a bad person deserving of his impending misfortune, but instead, by having made a series of mistakes leading to his downfall.
And that is Willy Loman in a nutshell. He began well, with a family he loved and a job that supported them, but he gradually pushes everything away through his affair, his poor salesmanship, his failure to show his pride in them to his sons, and his delusions.
He could have been a hero but pulled himself down by his own choices. He is not a wicked man, but he is not a virtuous man, hence he is a tragic hero in the sense that he could have been a true hero but destroyed himself.