Gratuitous murder undoes movie (SPOILERS)

I've seen a number of people bring up two major weak points in the logic of the movie (Eyal's out-of-the-blue marriage to Pia and his ability to bring a gun to Germany). However, there's a basic one that I haven't seen discussed. I don't buy Eyal's central mission.

Eyal is assigned to kill a man who's already close to death, on a rationally and morally flimsy premise ("get him before G-d does"), with no proof of the man's guilt other than his boss's say-so (and hints from Pia), and he expects to do so without a hitch. When he can't bring himself to do so, Axel steps in and kills his own grandfather without any qualms.

By contrast, in the movie "The Music Box", when Jessica Lange's character finds out that her father has been accused of Nazi-era murders, she struggles first to determine whether her father really was guilty, and then to decide whether it is her place to take his punishment into her own hands. These moral, emotional questions are thrust directly into the foreground, and they truly make us think. In "Walk on Water", they're meant not to be examined too closely for fear of making the plot unravel.

Eyal's murder of the terrorist leader at the beginning of the movie, cold-blooded as it may be, traumatic to the man's wife and son who witness the act, at least could be argued to remove another killer from the world (although, of course, there is a limitless supply of killers, and acts like this generally perpetuate the cycle rather than end it). But Axel's grandfather is not about to kill anyone else. To bring him to trial and force him to face up to his crimes would be one thing. To stroke his hair and turn off his oxygen without a word feels profoundly unsatisfying.

We're supposed to feel some kind of triumph as Eyal and Axel both exchange perspectives and grow. But if Eyal is growing in that he appreciates the ramifications of murder and is unwilling to perform a killing for the sake of vengeance, then Axel must be dying.