How does Hamlet's willingness to fight Laertes help solidify him as a tragic hero?

Hamlet has been, from the very first moments of the play, reluctant to carry out the absurd and generic task that is his as a character in a revenge tragedy – “The time is out of joint. Oh cursed spite / That ever I was born to set it right!” Shakespeare has purposefully miscast his hero and given us a character whose accomplishments are intellectual and verbal, not violent and physical. By the final Act, it seems as though the playwright has finally given up trying to tie his hero down to conventions. Hamlet has forced Hamlet off the rails, taken it from a simple and predictable genre play to something inscrutable, massively significant, and, for lack of a better term, post-theatrical. Laertes doesn't allow Hamlet to back down and accepts his apology without accepting the needlessness for the fight. Hamlet has no intention of participating. Thus, he is a tragic hero by default. He isn't really heroic at all.