I stated in my previous comment that if your assailant was too close, you may not have time for sight alignment with your handgun. If there is no time for sight alignment it would be stupid to try and align your sights with your firearm.
They teach the good old draw and shoot at your firing side if your opponent is too close. (I'll see if I can find a picture of the shooting position that I am describing.)
I don't know who "They" are,but somebody needs to slap some sense into them. You could miss a Buick at 10 feet if you're trying to shoot that way. Form a triangle with your back being the back side,your two arms being the left and right angles,and the centered handgun being the point. If you are holding it out in front of you and facing and looking at your target with both eyes,it's damn near impossible to miss. You need your eyes open and looking at your target instead of your sights so you can see where the bullets are striking him to adjust fire,and to see how he is reacting to the bullets that are striking him. If he continues to bring his gun to bear on you,this would be a excellent time for you to step to the side as you continue to face him and fire. You won't see him doing this if you are focusing on your sights. Neither will you see any of his buddies coming to his aid from the side. Or as far as that goes,if you are being attacked by more than one person,your ability to see the first attacker you are shooting going down gives you the instant option of transfering fire to his buddies. This could be worth a couple of seconds to you. Seconds that are vital for your survival.