The Night King got turned into what he is now by the magic of the Children of the Forest, but before this he was one of the First Men. Warging and Skinchanging seems to be limited to people who have the same blood as the First Men.
What if the Children of the Forest never meant for him to be able to control the dead? What if this was a side effect that they didn't expect? The Night King doesn't raise the dead by the Children's magic, he wargs into them.
Bran Stark has already been proven to be powerful enough to warg into another human being. I believe that the magic of the children enhanced the Night King's warging to be powerful enough to warg into all of his 'wights', dead people and animals, at once.
What if the magic of the children only allows him to turn people by touch, as he does with Craster's sons, turning them into White Walkers. This explains why they look different, and don't deteriorate like the wights. This is also why GRRM confirmed that "they are not 'dead', just an inhuman kind of life."
This could mean that Bran can still warg into them, since they are not dead.
This is what Bran is referring to when he says 'he must become stronger'.
Thoughts?