Why would you want to use the slide stop to release the slide?
Because it's quicker.
For many, it's more consistent and reliable. As mentioned, some people stupidly "assist" the slide forward, causing a jam or failure to lock into battery. Using the slide stop prevents that.
Further, if you had a shok-buff installed, (or the gun you picked up during the fight has one installed) you can't retract the slide far enough to disengage the slide stop.
Two reasons that I don't (teach the overhand method).....although I have nothing against this method if continous training is used by the shooter. (I prefer the "slingshot" method)
First: Shooters, under stress, will accidentally block the ejection port causing a Jam. This happens during clearing a miss fire or light primer strike or whenever you need to clear a round "already" inside the chamber.
If the student blocks the ejection port with their hand, they're doing it wrong. Grab the slide
behind the ejection port, palm down, thumb to rear and pull it back completely. It's not a difficult feat to learn, perform or remember.
Second: Shooters can have a tendency to "ride" the Slide when performing a reload .......... depends on the speed at which they can remove their hand. As you well know ........"fine" motor skills are affected first when under extreme stress ........ and what we see as simple movements can become difficult tasks under stress.
I'm presuming that by "slingshot method" you mean grasping the rear of the slide with thumb and forefinger, the left thumb being on the right side of the slide, the forefinger curled up against the left side. If you mean something different, please describe it. My comments concern my defintion.
The problem with the "Slingshot method" is that it requires several things to work:
1) Finger strength (many people do not have enough finger strength to pull slide back far enough against a 14# - 20# recoil spring that has the final, most difficult compression, using only two fingers with which to do it.
2) It requires
more fine motor skills than the overhand method.
3) If the fingers are wet with sweat or blood, a difficult task just became more difficult.
Again, it would behoove the serious student to learn both methods. If you pick up a downed cops Glock with the slide locked open and there is still someone to shoot at, that's a poor time to try and find the miniscule factory Glock slide release if you
only learn to drop the slide that way. Same problem the other way if the gun is a 1911 with a shok-buff installed.
If the slide doesn't go forward per your usual technique, immediately tranistion to the other one. Learn both, practice both.