Incoming, standard Dulvarian sized wall of text, complete with too many commas and parentheticals.
I use the SS after reloads, unless I hit the magic position and my Glock drops the slide without me touching it when I ram the magazine home. This is with all my pistols, and any pistol I have ever shot.
My Beretta Cougar (first carry gun) has an ambi safety, and slingshotting with that is liable to gouge your fingers enough to leave blood blisters. The SS is nice and wide. I have never missed it or failed to pick up a round when releasing. This is very similar to the Beretta 92 training mentioned above, for the same reason. Doing it with the safety OFF has a high probability of gouging your fingers, or engaging the safety. If you engage the safety, the hammer falls with the slide. You then have to take the safety off and fire the first shot DA. (And yes, I carried safety on. I practiced drawing and flicking the safety off and firing the first shot DA for hours on end until I felt comfortable doing it one handed, 100% of the time.)
My wife has an XD9 that I am making her proficient with. She has trouble with the slide release. As far as I know, and every XD I have ever handled, the SS took more force to release than other guns. So I taught her the slingshot method. It works for her. And after she pinched her hand doing it, I made her do it ten more times. The same skill will hold true if she picks up my Glock off the nightstand.
I have never had a single issue with any auto that I have ever picked up. I have never put any thought into using the controls, whether they be the mag release, SS, or safety. I have also never seen in person when using the SS did not successfully chamber a round with a properly inserted magazine. BTW, all the slingshotting in the world won't fix that error, and will likely cause the magazine to fall out, rather than just unseat more. (For what it's worth, once I seat the magazine, I leave my left hand holding the magazine against the gun while I release the slide. If it isn't seated properly, you will feel it move against your palm. A slight rotation from there with my strong hand and viola!, I'm holding in the Modified Weaver, certain that the magazine is seated and that a round is chambered.)
The only time that I even think about intentionally racking the slide is if it doesn't go bang when I pull the bang switch. Then it's T-R-B. I have never had an issue on the first round out of a handgun (centerfire). I have also never had a real stoppage that required a T-R-B other than when someone else loaded my mags with the purpose of inducing one for training. Which means I've never had one for real.
It does not matter what anyone, including me, says is a 'better method'. The correct method is the one that you have ingrained in yourself, with your brain and muscles and lots of repetition to develop muscle memory with the weapon you intend to use. It would take a stronger argument than "xxx school" teaches one way to make it reasonable for a person to change from their ingrained method. Like something that could potentially case them to shoot themselves in the hand while doing. We can all agree that such a method is both dangerous and wrong, and would probably either find cover or offer advice to the person we saw do it. Usually in that order.
Discussing probability that you will be picking foreign (to you) handguns off the ground, with loaded magazines no less, and how a particular method will work better in a hypothetical situation is kind of like every SHTF thread out there. (Unlikely to happen, and in the event that it does, there is very little you could have done outside of pure luck where your training would be of use.) Practicing with your gun, a lot, with a method that works for you until you don't even have to think about it is called 'training'. It doesn't have to come from a fancy tactical shooting school. It just takes time with YOUR GUN in your HAND and what WORKS.
I also call phooey on the fine motor skills not allowing you to get the job done. The 'examples' of people not being able to do something, like the dead aforementioned officer, is probably more of an example of being frozen or mentally incapacitated with fear or adrenaline. Training compensates for that. "Fight like you train, train like you fight" should sound familiar to a lot of people, for good reason. That is actually true, and is the only thing that I ever give as advice. So far, I have not found an instance where this did not hold true in any aspect of life. I'm only in my early thirties. I'll be sure to post if I find an instance that it didn't work. I might even write a novel (like most of my post lengths tend to indicate).
Without going into too much detail, the line of work that I am in intentionally and routinely runs ridiculously complicated drills on us with insanely high levels of forced decisions in very short time spans under high (forced) mental stress levels (that can be added to by people literally yelling in your face, or ear, as the case may be). When real situations happen, things tend to go very, very smoothly. Usually a let down from the drills, btw. Training to deal with high stress is possible, and I promise you that muscle memory can handle fine motor control for about thirty separate operations in the same sequential order, in under ten seconds. Nothing that I have experienced has required more than about than about thirty seconds of actions. And those that can't operate under those levels of stress find themselves in other places (in my job). And yes, my job has the one of highest arguable success ratios for these types of situations in our field, above and beyond any comparable civilian or other government agency.
*Disclaimer* Shooting sports where you are shooting at stationary targets and 'speed' is of the essence, one method may be 'faster' and may therefore be considered better. I concede this point with no hesitation.
*Question about disclaimer* If other targets are moving and engaging you with return fire, does anything matter other than your ability to hit COM on a moving target?
*Pure fantasy* That shooting simulator in GI Joe was awesome. Anyone know where I can get one?