Because it failed to do so. The Moment couldn't force the War Doctor to make his choice, and the War Doctor chose to kill. Now he didn't. It's not hard to see it happening both ways.
Hell, in The Name of the Doctor, War tells Eleven that he did something in the name of sanity and peace. And this is inside the Doctor's time stream, where Clara is able to interact with the actual different incarnations of the Doctor. So the War Doctor, who should know he didn't do anything if he never did anything claims to have done something.
So it happens both ways. First he does kill, then he doesn't. And the elegance of the second is that it fits perfectly as if he never had.
Setting aside that there is no evidence that The Moment failed at anything... How exactly
could The Moment fail? The Moment is still The Moment with a conscience and The War Doctor is still The War Doctor, with the exact same personality. In order for the event to play out differently despite the
exact same variables, the choice would have to be random. And there's no way that I believe that any incarnation of The Doctor would randomly choose yes or no to destroying two entire civilizations.
Now your interpretation of The War Doctor's words in The Name of the Doctor is really taking a strong literal interpretation on what can only be a symbolic scene. The War Doctor scene where 11 meets Clara can not be a literal moment from 11's life no matter what.
In the mystery location of the Time Stream that Clara lands, she sees multiple incarnations of The Doctor in that single place. If that location was a real time period in The Doctors life that she was reliving.. how were all those Doctors there at once? There's only one period of time where The War Doctor existed with other Doctors and we saw that in Day of the Doctor. The scene from Name of the Doctor could not have happened during that time.
The place that they are standing inside the Time Stream resembles Gallifrey during a time of war. But it can't be Gallifrey if Gallifrey is destroyed. If Gallifrey isn't destroyed yet, The War Doctor couldn't have known he destroyed it, right? So.. how does that work?
Okay, so let's say The War Doctor isn't standing on Gallifrey in The Name of the Doctor.. he's just standing on some other planet with some fires and a war like vibe going on. If The War Doctor had destroyed Gallifrey, he would still have regenerated immediately afterwards (the War Doctor generation was limited specifically to the period of The Time War) and we know from Day of the Doctor that when he saves Gallifrey, he regenerates before the TARDIS could even travel to another location. So he still could not have been standing anywhere after having destroyed Gallifrey.
Any way that you look at this, there's far more evidence for the entire event being circular... always happening the same way each time. You theory requires beliefs and interpretations that are more tenuous and have more gaps than the circular theory. And the circular theory has support in Moffats previous writing as well.