At the end of season 7, Jon Snow refused to commit to staying in the north and not taking up arms against the Throne. Everyone in Daenerys' party thought that his integrity was too costly under the circumstances because it gave Cersei a reason to back out of an armistice.
Given the discovery that Jon had a Targaryen claim to the throne which was senior to Daenerys' claim, if Jon did make that pledge, would it not amount to giving up Targaryen's claim to the throne altogether? Wouldn't it reduce Daenerys' claim as well?
Or, rather, would his claim only extend to his function as "King of the North"?
Sansa presses Dani, at the end of s08e02, trying to commit Dani to recognize that the North is free.
But, if Dani succeeds in taking the Iron Throne, given that Jon has Targaryen lineage, and that he was named "the king of the North", wouldn't that make the North pledged to the Throne because it is pledged to Targaryens?