I haven't been able to find a satisfactory answer regarding why it's said that solid tongue and groove, nailed down wood floors should not also be edge grooved along the tongue and groove, which should help prevent gapping and water from making it's way down in between planks.

Some say its because the movement of the wood will break apart the glued joint, which makes no sense, since glued joints are stronger than the rest of the wood.

Many have used glued in dutchmans and shims to fill in gaps that have developed in between planks, with no issues I've heard of.

Others claim gluing them would fight against the wood's movements, creating issues, but no explanation on what exactly are they proposing this would result in.

I just would like to understand exactly how this would cause failure and the mechanism behind it. What do you think?

Edge gluing between strips of flooring is just unnecessary and takes extra time when laying a floor. It makes replacing a bad board very difficult.
Properly acclimated flooring will not need edge glue to hold it in place if fastened properly. If there are such big gaps between rows of flooring after the floor dries out after acclimation glue would cause the strip to break along the grain, not just at the T&G joint. Big gaps are usually caused by laying "damp" flooring that has not been stored properly after delivery from the manufacturer.
If you have so much water that it goes down between the boards glue would keep the water in place under the boards so it would take longer to dry out which may cause a mold problem, or cupping that would not get flat again.

Pete, thanks for you input! Sorry for the late response, it's the holidays, I'm sure you can understand.

I understand that properly acclimated and properly installed nailed flooring, as well as maintaining consistent indoor climate control throughout the year, will address gapping more than anything else, but I've wondered why not also edge glue for the extra insurance, to make an installation more foolproof, if you will. For example, apartments built in northern climate that won't have an hvac system or any kind of humidity regulation. Even properly acclimated wood flooring will likely develop some degree of gapping.

Also, consider that, unfortunately, it seems that like the common installer with an average level of skill and workmanship are not likely to address common installation issues, such as how to properly install the last planks close to wall, where a floor nailer can't be used. Most just hand nail it and call it done. The common consequence being that these planks often become very gapped.

Now, what you're saying is that if the planks were glue together, when there's expansion and contraction, something will give, and it may not be the glued joint, but cracking will occur somewhere along the grain of the plank. Do I have that right? I've had the thought that something like that might happen, but I haven't been able to find anything online that has demonstrated this. I'm thinking I'll have to create a 4'x4' test board of wood planks nailed and edge glued onto plywood, and subject it to intervals of high humidity and drying, and see what happens.

Its just been a bit odd trying to figure this out theoretically, because I can make just as many arguments that nailed and edge glued planks will crack along the grain, as I can that it would instead actually force the planks to expand and contract as a contiguous whole. Also, taking into account that wide floor planks are commonly recommended to be edge glued in addition to nailed. Are reports of cracking as a consequence common? I personally don't like the look of wide boards, its 2.5" max for me or nothing, so I haven't paid attention to them.

It is a recommended practice to glue and nail planks over 5 inches wide. The reason for this is that there are fasteners only on the edges of the planks. The glue under the planks will help keep the flooring fastened down better. The edges are not specifically glued, although some glue may fill the void between the planks as they are pushed together sliding in the wet glue layer.
I find that when a mechanic is finishing up the last rows next to the wall and they like to blind nail because the automatic nail gun will not fit the edge gets deformed a little from driving the nail by hand or shooting a nail in at an odd angle. This keeps the boards from sliding together without significant force which can leave a small gap. This is why I sometimes see the last 5 rows just top-nailed. It is faster to finish this way without blind nailing.
I have never seen edges glued along with the mechanical fasteners. When installing a floating floor the glue is placed carefully so no glue gets forced to the surface. It just stays in the T&G area of the joint. This is done with an engineered floor which does not have the expansion and contraction issue because of the way it is made, having such a stable base of plywood construction.
You will have challenges making a sample that could develop gaps if your plywood is not fastened securely to framing, I think. Fastening to loose plywood can deform the plywood in my experience.