Let's look at the Benelli Vinci; one of the newest of the breed and made to work with a wide range of available ammo.
Page 38 of the owners manual (available on line) says:" In-depth ballistic laboratory experiments, and specific practical tests confirm that for correct firearm function, the kinetic energy value developed by a 12 gauge cartridge is 230 kgm - value measured on manometric barrel with speed V1 at 1 m from the muzzle.
That energy level translates to approximately 1665 lb. ft.
If we look at Remington 8 pellet reduced recoil buckshot which has a MV of 1200 fps. you will find that it develops approximately 1400 ft. lb. That falls short of the minimum energy floor for reliable operation as stated by the manufacturer.
If you look on line at the Benelli M2 they state that it will function with all 1 1/8 oz. loads. That statement is found right on their website. That leaves 8 pellet 00 Buck, 28 gr., and 24 gr. loads in question. They may or may not cycle the actions.....YMMV.
Once again: Semi automatic designs have operating parameters based on their designs. Whether Inertial or Gas operated, you need to work within those parameters. If you fail to work within the window for which they are designed you will have malfunctions. They will either not cycle properly or you will beat the hell out of them. Just because one make / model works within a particular window does not mean that another make / model will do the same.
To imply or state that because item A works outside of the specified window means that item B will do the same is pure nonsense. All you have to do is a little research of the different manufacturers websites to see the folly in those types of gross oversimplifications.
If you operate a semiauto with ammo that it is rated for, they generally work and work well. If you use ammo outside of the operating parameters for which they are designed, you risk either damage or making it a one shot repeater.
I guess I'm not sure of the point of your post. If it's read the owner's manual and it will tell you the operating parameters - that's much easier and shorter than the opus you feel is needed to explain the function of a semi-automatic.
If your point is - every semi-auto operates within different working parameters because of individual design differences - again, read the owner's manual.
In my case, with my semi-auto, I have had the gas pistons modified so that I no longer need to change gas pistons for light (less than 1-1/2 oz loads) and heavy (1-1/2 oz loads and heavier).
I can now use the heavy gas piston for loads down to 1-oz. It will not cycle 7/8-oz loads with the heavy gas piston. To use 7/8-oz loads I would have to change to the light gas piston.
I know I am not going to "batter the gun" shooting heavy loads as I am using the heavy gas piston, and the gun is rated for 2-3/4-inch to 3-inch magnum shells as stated in the owner's manual with no limits given on maximum shot weight. Meaning, it's rated to function with commercially loaded ammunition in those two shell sizes. You cannot use 3-1/2 inch shells in the gun as stated in the owner's manual.
There is also a caveat in the owner's manual stating that some ammunition with shot weights less than 1-1/4-oz may cause the gun to not cycle. So far, having shot nearly 2,000 rounds through it including at least 20 trap sessions with 1-oz loads, the gun has never malfunctioned.
For personal defense use, given the manufacturer's function statement, I would never shoot any ammunition that has not been tested in the gun. In my case, that includes testing three brands of 00 buck, two brands of 000 buck, three brands of slugs, and Winchester PDX.
I really don't think this is as complicated as you seem to want to make it - and I don't think that anyone posting in the thread has stated that you can ubiquitously apply any statement to all semi-automatics as you want to imply.
I think this is about as simple as stating, "you need to read the owner's manual to find the funtional requirements and operational parameters of each individual shotgun, as each manufacturer's semi-automatic shotgun design is different."