In the season seven finale, Bran says, "He's never been a bastard. He's the heir to the Iron Throne." It's an amazing moment, but Jon's path to ruling the Seven Kingdoms isn't that simple. He is the true-born son of Rhaegar Targaryen and Lyanna Stark, so he would be the next Targaryen in line if Robert's Rebellion had never happened. Just because the legitimate Baratheons are all dead, doesn't mean Westeros has to default back to the Targaryens.
However, Jon could take the throne by force, or he could simply win the favor of the people. The Targaryen name is associated with fear after the Mad King's reign, but with Jon positioned to be the hero in the coming war with the dead, the populous of Westeros may be more than happy to have Prince Rhaegar's son on the throne. The man was declared King in the North when he was still a bastard, so he certainly inspires devotion. Saving the entire realm would surely lead the people to forego the tricky nuances of succession and submit to a new Targaryen reign, led by Jon — err, Aegon — who is both a wolf and a dragon.
