I can understand saying it was rushed and poorly done, but the trained assassin, who serves the god of death, absolutely should have been the one to kill the night king. No one has a bigger beef with death than the undead army master.
Jon came back to kill Danny and take the throne and restore what passes for peace.
The Three Eyed Raven took it from Jon.
None of this was especially well laid out or planned or paced correctly, but it’s the most Game of Thrones path they could’ve taken.