*ATTENTION NEW THEORY*
BRAN IS LITTLEFINGER (and will sit on the iron throne). I was rewatching last season and I realized that the interactions with Bran and Petyr Baelish were pretty weird. At one point, Bran says a direct quote that LF said to Varys in S1; “Chaos is a ladder”. Why is this important and why does this mean Bran IS Littlefinger? Bear with me: We know fully well that Bran can warg into animals and into people, right? We’ve even seen Bran warging into people and causing events in the past (see Hodor).
What if Bran was connected to Littlefinger all along and he conspired all along the way to have the realm go into absolute chaos by using Baelish as his “host”.
I believe the Night King saw this and was trying to stop it, hence why he gives Bran such a surprised look when he was about to kill him, he was like “damn, this guy is messed up”. Anyways, Bran controlling LF would also explain why Peter is so fond of Catelyn Stark. Now, if this theory was to be true, why would Baelish send an assassin to try to kill Bran? Simple, he was trying to break free from Bran’s possession.
Why did Bran allow LF to die then? Well, he had served his purpose of creating chaos in Westeros and passed on the mantle to Sansa to be the chaos creator of the realm. My prediction is that Bran will take advantage of the events from S8 and have Khaleesi kill Tyrion, Jon kills Khaleesi and then either Jon going to the north or Jon being killed by someone else.
I predict Bran is doing all this so he can sit in the Iron Throne.