Jon Snow is no longer Eddard Stark’s bastard son. Through the course of the series, we’ve seen him grow from the bane of Catelyn Stark’s existence to Lord Commander of the Night’s Watch to the King In The North.
As we now know, Jon Snow was never really Ned’s bastard. He is actually the son of Rhaegar Targaryen and Lyanna Stark and as such has a legitimate claim to the Iron Throne as the last remaining male heir to the Targaryen dynasty.
He may very well be, in fact, the one rival to the Iron Throne with both the birthright and the leadership skills necessary to see Westeros through the incredibly dark times ahead.
During his time at the Wall, Jon was able to prove himself a great swordsman, and a man of honor willing to stick up for those with less skill than himself.
During his time with the wildlings, Jon gained the trust of a group of people known for being extremely untrustworthy of outsiders, eventually convincing some of them to come to the aid of those south of the wall.
It’s important to note that not even death has managed to defeat Jon Snow. After he was betrayed and killed by his brothers in the Night’s Watch, with the help of Melisandre, Jon was resurrected.
Jon is, however, not craven or power hungry. He’s only accepted the role of leader grudgingly and even walked away from being Lord Commander after his betrayal and death.
With the inevitable invasion of Westeros by the Night King and his army of White Walkers, Westeros is in desperate need of a no-nonsense leader, as skilled in combat as they are in strategy that truly understands the need to do away with politics and scheming and band together to fight this existential threat. Jon Snow is the only one who understands this. If he’s not able to convince his two rivals to the throne of this fact, it may ultimately fall on Jon to be the leader Westeros needs most.