Im an upstate NY cop.
Last time I was in a shoot out The first 13 rounds were point shooting at about 10-12 yards while moving. I remember looking through the gun, like i trained. I utilized my sites after a reload. MY opinion from military and police experience is surprise engagements use muscle memory. situations in which u have a second to formulate a plan give u time to utilize your sites.
Keep in mind my memory of details only came after a few nights sleep, and talking to my partner and witnesses at the scene.