Coming round to the theory that the 3 eyed raven is an absolute wrong-un who was actually imprisoned in that magic tree north of the wall. The NK came south of the wall to execute him, or 'bring him in' I suppose.
So Bran will turn out to be the big evil boss who is manipulating everything.
Episode 4 will be an 80 minute corker, I think.
I have genuinely wondered for a long time about Bran/The 3 Eyed Raven. I don't know why people assume he is a force for good, he doesn't show much to indicate that.
As you say, The Night King only cared about Bran. Didn't even bother to kill Daenerys or Jon when stood right in front of them. More to learn about that boy yet.