After everything John has been through, I don't think he would just give up like that and stand there for the dragon to kill him. He obviously knows he is no match for the dragon so he could have just left it and kept trying to move towards the Night King which he had being doing the whole episode. But he stayed with the dragon instead.
I will honestly say that I refuse the satisfaction of the showrunners cheapening the death of the Night King. If you know, Jon was flat on his back prior to yelling at the dragon, “GOOOOO – GO – GO” or was it “NOOOOO – No – NO’? Don’t know really, but now due to one person’s reddit post, everyone must be made to believe this theory, but we all heard “GOOOOO – GO – GO” right?
Arya had to make quite some ground from where we last saw her, and between that and Jon’s dragon scene we now need to accept this, no. Maybe the scene is too dark, will try to follow one of the thousand guides now available of correctly tuning your television for this one episode as it should be tuned now for absolutely everything, because HBO.
What really grates me, after this one episode, the Night King had no reason whatsoever to come South of the wall. He already marked Bran and could have taken care of Bran North of the wall at any time since then. We don’t even know why they stopped their previous war on men, we don’t even know why he wanted to kill the Three-Eyed Raven. What was the motivation of the Night King, other than illustrating global warming?
Like the many other critics of this episode, nobody has a problem with Arya killing the Night King, it was how it was done with no substance other than portraying her as, on the spot, Azor Ahai. Jon should have been more involved, there should have been more story to the Night King, than someone theorising “GOOOOO – GO – GO” in probably the ‘darkest’ scene in television history if don’t know how to properly configure your television or monitor that is.
I wouldn’t be surprised if it was a staff member of HBO dropping the ‘hint’ on reddit.
Here is the scene for those with interest,
just remember to tune your display with HBO 'proper' specifications.