I am not suggesting that John should have become king. I am suggesting that it is strange that it is never even mentioned in the final episode of the series. John's whole arc seemed to be the backbone of the show. They didn't do his story justice in the finale.
Jon Snow was the tragic figure in this show.
He was born regal, but told he was a bastard.
He was lied to (for his own good), and told he was less than those around him. It's not clear why Ned wouldn't tell him who he was when he was a grown man, or after Robert Baratheon was dead, but it at some point it's just gratuitously harming him.
Because of the lies he was told, and never corrected, he joined the Night's Watch, where he had the promise of being celibate and lonely for the rest of his life.
He's a genuinely good dude, and cares about people, and for that he is treated with open hostility by much of the guard.
He saves wildlings from the wights, and the night king, and is murdered for his kindness.
He then endures the torment of being brought back to life, where he again faces scorn and ridicule from his killers.
He watches his brother get cut down at the B of the B, and then is almost killed before being saved.
He then commits himself to fighting the NK for the benefit of everybody.
He falls in love with a woman, only to find out she is his aunt and bat crap crazy.
He removes the greatest danger to the people of the world, for which his punishment is imprisonment and then exile.
In the end, he may have been the only truly good character, and his character arc, which was constant sacrifice for others without concern for self, was constant and perfect.
