The subject of Game Of Thrones can sometimes be a bit of a sore one. Some will dismiss the season entirely, others champion there being a few good jewels to be kept from it, while still others (although the minority) will defend the final season to the very end.
While the entirety of the season can be too big a bite to chew, it's still great fun to break down the smaller aspects of the season--why miss out on the smaller debates just because of the greater one? One such debate is the matter of who should have killed the Night King. Was Arya the fitting choice? Or should it have been someone else?
Jon Snow
Jon Snow was the most obvious choice of who would end up conquering the Night King. Jon Snow is the one who raised awareness about the threat of the White Walkers beyond the wall.
He is the one who risked his life several times for the cause of preparing for the war against the army of The Dead. Many would say that these reasons give Jon Snow the right to be the one who defeats the Night King.
Arya
Of the many reasons that Arya is a fitting choice to have as the Night King's assassin, the first is that she is simply more focused than anyone else in the battle.
Jon Snow may have fought the White Walkers before, but he has since become distracted by his relationship with Daenerys, and even before then, he expressed time and time again that he was exhausted from fighting all of his life. Arya is younger and a more keen fighter than Jon at this point in the series.
Daenerys
Daenerys has not been in Westeros long at the time of the battle, but the fact remains that she has the greatest degree of control over her two remaining dragons.
The Night King has spears with which he can kill the dragons, but he can only throw these so fast, and we don't see him holding many. One would think Daenerys could use her dragons to swarm him and then go in for the attack, a major symbolic move of fire destroying ice.
Arya
Arya killing the Night King was a great moment for the show in of the accomplishments of female characters.
Arya knows from childhood that she is a fighter. She stays true to this determination all of her life, and the act of her successfully killing the king is a way of undeniably asserting her identity as a fighter to the world, and with it, female power and agency over their own destiny.
Bran
While Bran may be one of the lesser rooted for options--he doesn't do much to spark our enthusiasm once he becomes the Three-Eyed Raven, to be fair--it would make perfect sense for him to kill the Night King.
In fact, it makes little sense that he didn't. It would put him at risk, it's true, but his ability to inhabit other bodies would enable him to trick the king and defend Winterfell, instead of sitting by doing nothing.
Arya
By the time of the battle, Arya has freshly left her training in Braavos.
While watching her train, it didn't seem immediately apparent to the viewer that the skills she was learning would so greatly distinguish her from other fighters in Westeros, but when she returns he focus and quickness proves great enough to allow her to out-wit anyone who challenges her--including the Night King.
Jaime Lannister
Jaime Lannister being the one to kill the Night King would have been a great twist in the story. He has already gained much viewer approval at this point through his resistance to Cersei in honoring his word to fight with those at Winterfell.
Jaime killing the Night King could have been his final act in transforming himself into the alternate version of himself that he has gradually worked on the entire series. Alas, his destiny goes no such way.
Arya
Arya left Braavos as Arya Stark, but she also, for some reason, was allowed to leave with a bag full of faces.
She is able to use the faces just as a Faceless Man would; enabling her to put on a face and not just resemble that face, but to embody the person it belonged to entirely. By doing this, she could better sneak her way closer to the Night King.
Brienne Of Tarth
Brienne would have been an exciting choice to have kill the Night King. She doesn't have much connection to the cause, having only recently been made aware of it, but viewers know her to be the most duty-bound, no-nonsense character in the show.
She would sacrifice anything to protect the greater good, and while the sacrifice of her own life to kill the king would have been sad, it would have made for a beautiful finish for her character.
Arya
In many ways, Arya seems like a random choice for killing the king. She spent most of her life outside of the north, after all, and most recently was working to annihilate her identity as a Stark by taking up with the Faceless Men in Braavos.
One might consider, however, the way the Faceless Man looked at her when she reclaimed her Westeros.