I meant to address this earlier.It lets you have the finger at or in the trigger guard at the point of draw, which allows you to get the pistol into play faster, with less movement.
It 1) doesn't put the pistol into play any faster and 2) the amount of movement is exactly the same.
I'll address the second point first. At some point in the presentation, the finger must move from being off the trigger to being on the trigger. I'm not sure how you are seeing less movement if it goes on the trigger before it is pointed at the target.
It is much safer to access the trigger after the muzzle has been rotated from the vertical to the horizontal. It must be rotated before a shot should be fired. If the finger is placed on the trigger after, or during, the rotation, how is it any slower. If you extend the gun before firing the first shot, there is plenty of time between Position 3 and Position 4 (in a 4 step draw) to access the trigger.
During testing in the late 60s, they found that there was no difference between the times, to the first accurate shot, from a holster, between a DA revolver, DA/SA pistol or SAO pistol