And the people who killed them, Sansa and the Umbers included, would know about Rickon.

It seems apparent that women can take the family seat if there are no eligible sons (like Bronn’s erstwhile wife inheriting her castle); Jon said that Sansa was the heir because he believed that Bran and Rickon are dead.

Why would she get more supporters than Rickon? If Bran is gone, Rickon is the rightful heir. As far as I can tell, no one has any reason to dislike him.

The Boltons know Rickon is alive. Sansa knows Rickon is alive. The Umbers know Rickon is alive. If and when the Boltons are overthrown, they would have no reason to withhold this information.

How does Bran being gone establish precedent for Rickon being passed over. There’s a line of succession. Rickon is ahead of Sansa in it.

Bigger army? Sansa’s army is four people.

I might cry beforehand, since for it to happen would require the violent death of her 8 year old brother, Rickon.