A Targaryen Marriage Could Be The Answer
Should Jon Snow manage to defeat the White Walkers, usurp Cersei, claim his heritage as a Targaryen, and sit atop the Iron Throne, there will still be a problem unsolved: Daenerys Targaryen, as well as her two dragons. Since Game of Thrones season 1, Daenerys has been fighting to return to Westeros and claim the Iron Throne, and it's unlikely that a surprise nephew is going to make her give all of that up. A battle between Jon and Dany would simply continue to tear the realm apart, but there's a simple solution here: a marriage, ending with the two ruling as King and Queen. Given the two have already developed an intimate relationship, this would seem to be a solution that they would both be happy with, and it solves a lot of the problems with either ruling solo.
Daenerys, although a Targaryen and a dragonrider, doesn't know Westeros (as Tyrion has previously pointed out to her). Nor do the smallfolk (or nobles) of Westeros know her. However, they know the Starks, and they know the Night's Watch, and they know Jon Snow. His connection to Winterfell would allow him to leave Sansa as Wardenness of the North, secure in the knowledge that they are on the same team, and his history with the noble houses would help them keep the peace. At the same time, having Daenerys married would quiet those nobles who would not want to see a woman rule, or a Queen who has spent her life outside the Seven Kingdoms. It seems like a perfect match. Of course, there's always that incest issue - but that Targaryens have married within their own families for hundreds of years, which has to count for something.
For The Good Of The Realm
At the end of the day, of all the characters in Game of Thrones, Jon Snow may be the most straightforward, purely good person in Westeros. He's not actually interested in the Iron Throne, he's interested in peace. He has little time for games and politics, and when he has to kill, he does so without torture, brutality, or enjoyment. He has also the knowledge, the lineage, and the connections, and he would seem to be an obvious choice for the new King.
However, Game of Thrones is rarely as straightforward as all that. Other theories as to Jon Snow's fate in Game of Thrones season 8 include his death at the hands of Daenerys, him revealed as Azor Ahai, his betrayal by someone else close to him (Sansa, perhaps), and even a return to the Night's Watch as new Lord Commander. For a show with this many twists and turns, it's impossible to say which way Jon's story will unfold, but if it comes down to simple worthiness, he should definitely end up on the Iron Throne at King's Landing.