It could also explain the NK's weird fascination with Jon Snow.

Probably because there are two Night's Kings. One is the First Stark King of Winter, and the other is Robb Stark who is the new Long Night's King. He's the baby Other we see created in the show.

Lady Stoneheart sets up the cost of being brought back too long, and Varamyr Sixskins shows how a warg's spirit wanders looking for a place for second life and what happens over time after you're dead. The wright also recognizes Varamyr in second life which indicates the wrights are being warged. The living lose their minds, but if the body is dead with the soul nearby it can be warged into forcing the soul to return but control is fully in the warg's hands with the soul as a passenger.

Robb would come back as a King seeking revenge filled with complete viciousness and hatred with his humanity stripped away. His Second life in Grey Wind lasted for minutes of rage before he was murdered again. People were what betrayed him and the living are his enemy. Just like Lady Stoneheart seeks revenge on anyone connected to the Red Wedding, but don't care if they actually were or not like Brienne or Pod.

It's also why you never see the full Other crew at once. It's always a Night's King, and 3 or 4 White Walkers accompanying him but never the full strength. Divide and conquer with one dealing with the Wildlings and the other with the CotF.