Let's look at the assumptions you are making now...
1) You assume you will be in the immediate vicinity of the shooter as soon as he begins shooting. Otherwise, it would not require Jesse Owens to grab a gun and arrive on scene before you could accomplish your feats of legendary shooting prowess.
2) You assume that you will see the shots fired, yet be in position to draw and engage before you are noticed by the shooter.
I have one friend who has responded to an active shooter. He was not in the room where the event started. (School, in SoCal.) He was the first deputy to arrive on scene, and he chased down the shooter, solo, instead of waiting for backup. He told me that Columbine was still fresh in everybody's head, and all his peers had agreed they would not stay outside while an active shooter did his work.
But the point is, he was not right there when the shooting started, but instead he ran to the threat.
So, for your arguments to hold water, we have to assume you will be virtually on top of the shooter, in a position to observe the shooter, yet screened from his awareness when he starts his rampage.
Take one or two of those assumptions away, and your arguments fall apart.
I am not saying not to engage. I am saying you really need to positively identify the threat, not just identify that a guy has a gun. I am also saying you need to brush up on deadly force laws, because some of the things you are espousing, such as not accepting surrender, period, would put you in prison.