The issue with the story is not who killed the Night King, its the fact that the character of the Night King was left only partially developed. He was left as a prop that was only useful to Jon Snow's, Bran's and, to a lesser extent, Dany's development (but
nothing toward Arya, she wasn't forced to grow at all due to him before killing him). So him being killed by the person who was developed least by him left us with no emotional character growth to think about except the Night King's character itself. And when you're forced to think about that, you realize you know next to nothing about him, or why any of this was happening.
At least if John or Bran or even Dany had killed him, at least we'd be thinking of what the Night King had done to those characters at the end, their
resolutions would be an emotional apex for us. We'd get to see how John had grown from the challenges he faced from this 'monster' throughout the seasons, and at least we'd get some amount of empathetic emotional reaction to that climax through empathizing with John or Dany or Bran and what they must be feeling at defeating this monster that had taken so much from them and had put them through such misery. When Arya does it, we don't have any reason to feel like an emotional resolution happened with her. She lost almost nothing due to him, and frankly none of her growth was because of his actions, because her struggles were not against him. He may as well have been fucking hit by a bus. So after he gets hit by the Arya bus while crossing the street, we're left thinking 'what the fuck was the Night King's deal? Who was he? What was his plan? What just changed because that bus hit him, what possible futures were just undone---and all those questions are left with very unsatisfying answers because we do not know shit about the Night King. He's just a shallow, monster of the week...
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