Could Bran Stark be the rightful King under certain circumstances?

Question

By Rhaegar and Lyanna's marriage the Starks are now technically members of the royal bloodline. Therefore if by some twist of fate Jon ends up killing Dany and goes to live in the north renouncing his claim, would it be correct to say that Bran would now be the rightful king of Westeros? He is the nephew of Jon Snow(Current rightful king) after all. He could rule with a regency such as Aegon III did with members being Tyrion Davos Sam Bronn etc.

Put simply, would Bran Stark be the rightful King of Westeros in the event of Dany's death and Jon Snow's self imposed exile?

Discount Gendry, assume that he remains a Bastard/is forced to give up him claim via Rhaelle Targaryen.

Answer 1

TL,DR: The Starks are not members of royal bloodline, only Jon is

Lyanna's branch of the Stark family is related to the Targaryens, but Eddard's branch have nothing to do with them.

In other words, Bran has no Targaryen blood, and has zero claim to the Iron Throne.

Also, Bran is not the nephew of Jon Snow.

Jon Snow is the son of Lyanna, sister of Eddard Stark. This make Bran and Jon cousins, not nephew and uncle.

What could happen if the last known heir dies?

The case where succession is unclear has already happened several time in history of the Seven Kingdoms, and in such cases, the Great Council is summoned, as it was the case for Aegon III.

If Daenerys dies, and Jon Snow/Gendry didn't claim the throne, and the Iron Throne became vacant, such a thing may happen.

As a side note, it become quite clear in recent episodes that

Bran Stark is not really Bran Stark anymore, but the Three-Eyed Raven, and doesn't even want to rule Winterfell and the North, even if he is the true heir, behind Jon, Sansa and Arya.