As an engineer I see it like this. Imagine I send a wave and then I send another wave in phase shift to cancel that wave. Unless I am sending the wave from exactly the same point in both instances, then I will not have perfect destructuve interference everywhere. Now if I do send the wave and the phase shifted wave from the same location, then it is as if I try to push a cart and pull a cart at the same time. The forces will cancel out and there is no net energy or force. The point I am trying to make is that in practice there will be a small separation between the origin of my two waves and hence there will be areas of destructive and of constructive interference as I cannot perfectly overlap the waves. Does this make sense to you Physicists?
You are right about what happens in reality. But physical models are simple, and generally, they don't care about practical nuances like this.
So, according to any physical model, even when you emit two waves like that (from the same point, with precisely the phase difference that you want), the mathematical background implies that the model should hold.
Thus it doesn't matter what happens in reality, from the point of view of the theoretical framework. In fact, these kinds of thought experiments can even be used to test the validity of the model, because the model's predictions shouldn't cause any contradictions to the assumptions on which it is based.