I would have still considered her a remote possibility... but she proved this season that won't happen. Not only does she absolutely abhor it... she told Sansa how she'd kill every lord who disagreed with Jon. Like... that's worse than Joffrey. She wouldn't last a day with that attitude.
Is OP talking about the books or show? Because for all practical purposes, they might as well be treated as two completely distinct and unrelated entities who happen to have characters sharing the same names. The complete and utter bastardization of Arya in the show is a great example of this; ShowArya and BookArya really don’t have much of anything in common anymore from both a story arc and characterization perspective.
I hear you, but the creators and GRRM have made sure that the major plot points are in sync. For example, once the shows passed the books, GRRM told them about "Hold the Door," burning of Shireen, R+L=J, etc., to make sure that there wouldn't be any major convergence.