We say, Allahu alam because we know we are faulty creatures with imperfect faculties.
More often than not, we fail when trying to discern right from wrong. We do not always see how the good we do today, may lead to evil tomorrow, and how the evil we perceive in others, may one day lead to good.
When we say, God knows (best) we acknowledge our judgment is murky at best and our knowledge limited, even though our ego is always trying to convince us otherwise.
By humbling ourselves this way, we allow for a moment of contemplation. A pause that sometimes may prove enough to help us see more clearly.
Thus, with every Allahu alam we utter, we give ourselves a chance to become hopefully less imperfect than we otherwise would have been.