Your OP is based on pretty lame straw man. I don’t think anyone seriously believes that ALL disease begins in the gut.
I’d like to see the evidence that there is wholesale mineral and micronutrient deficiency resulting from “modern processed diets”. This is the kind of thinking that makes vitamin manufacturers chuckle all the way to the bank, but has very little evidentiary basis.
By the way, while I am highly dubious of the claim that “all disease begins in the gut”, I am pretty confident that all poop begins in the gut. 
The only thing all diseases have in common is life. After that, it’s a crapshoot, which is guaranteed by complexity.
Any theory that posits that all disease has a common source (other than life itself) is hogwash.
Huh?
You are dubious that a diet, any diet, high in fruits, vegetables, nuts, fiber, fish, etc., and low on sugar and highly refined carbohydrates, is an improvement on the Standard American Diet that overloads on calories, fat, and sugar? Really?
No question that there is strange stuff on the GAPS diet list, much of their to avoid list are very healthy foods that in fact have great evidence as foods that encourage what is generally thought to be healthy gut bacteria. No barley, buckwheat or bitter melon? No beer!? No chick peas? No okra or potatoes either white or sweet? Only very ripe bananas? They specifically tell people to avoid fructo-oligosaccharides (FOS) which are well established as prebiotics?
Strange restrictions and the little real science (there is an apparent interplay between diet, the microbiome, intenstinal permability, inflammation, and distant effects on allergy, autoimmune diseases, and even effects on the brain, the understanding of which is still in progress) that inspired this bit of woo is well lost in a surplus of silly pseudoscience.
Nice that in fine print they state:
Dude, it’s the catchphrase I keep seeing from them.
I wouldn’t worry too much about micronutrients until you were sure that you were getting all of the major ones and there’s little doubt that most if not all people relying solely on diet are at least marginally deficient in one or more that are important.
Let’s talk just about essential minerals for example. Start with zinc. Look at the DV and then look at the best sources. Well that looks easy right? Assuming your diet is high in animal protein and assuming the animal protein is beef or shellfish. Maybe you can eat the latter everyday with no problems but the former will probably present other issues.
That was an easy one though. Let’s look at magnesium. Hope you like to eat lots and lots of nuts, bran, spinach, oh, and more nuts.
I could keep going down the list but I’m lazy.
This may be a little bit old but I doubt things have improved over the last decade plus. Energy dense nutrition poor foods, i.e. the Stadard American Diet, are clearly associated with not meeting RDA for a variety of micronutrients. See Table 4. The majority are below for folate, A, C, and calcium, for example. The higher tertiles for EDNP foods the worst. it reflects in serum levels as well (see Table 5).
“Wholesale deficiency”? Depends on how you want to define it. Retail level maybe. But the Standard American Diet is not at the levels advised for many micronutrients mainly as a result of energy dense nutrition poor foods being common at the expense of less energy dense and more nutrition rich choices.
Why couldn’t it be that all disease begins in the gut? Hippocrates suggested this thousands of years ago. Maybe in his time, with less human made influence on health, it was easier to accept. And now, why wouldn’t the gut at least be a stating place for some health problems? Or, because the statement is too absolute, you write off the entire idea?
Because it’s been proven otherwise. For a trivial example, you catch malaria from infected mosquitoes.
Try looking up Falsifiability and the Scientific Method.
Zinc and magnesium are not just essential nutrients (in small amounts) to you, they are essential to pretty much all other living things too. What is more, as chemical elements, they are not destroyed by cooking or most other processing. Thus, except for highly refined “foods” such as sugar, practically all foods are going to contain biologically significant quantities of magnesium and zinc.
Beef and shellfish might contain slightly more zinc, proportionally, than other foods, and nuts, bran and spinach might contain slightly more magnesium, but they are very far from being the only dietary sources of these elements, and it is nonsense to suggest that we need to eat these foods in order to get enough. Indeed, I should think that it would be almost impossible to get a magnesium deficiency unless you were starving anyway from lack of calories and protein, and very difficult to get a zinc deficiency either.
I haven’t been through the list you linked to, but I would be surprised if the same considerations did not apply to most or all of the nutrients listed there. Most if not all nutrients necessary for humans are necessary for most other living things too (whether as stuff they need to take in, as food, or through the roots, or as compounds they synthesize themselves, within their cells) so they are going to be available in virtually all foodstuffs. It is not generally necessary to seek out foods that are especially rich in some particular nutrient in order to get plenty enough of it. (The only real exception is some vitamins, such as C, that may be destroyed by cooking. To get enough vitamin C, and perhaps some other vitamins, it may be important to eat a certain amount of raw food, and if you don’t want to eat too much raw stuff, it may be best to eat raw foods particularly high in C, such as fruit.)
No, we just write off the foolish absolutism.
News flash: there is an entire medical specialty devoted to diseases of the gut - it’s called gastroenterology.
Yeah, well, that’s not true at all… unless you have a cite?
It starts with Candida, but pretty soon you have Knock Three Times and even Tie a Yellow Ribbon Round the Old Oak Tree. Candida is nothing to laugh at.
You have never dealt with wooish health types, I guess. They are all aiming for a Grand Unified Theory but they all miss out because they can’t unify on the one thing that causes all of Mankind’s ills.
Pythagoras wouldn’t allow his followers to eat beans. Aristotle believed that the Sun, Moon, and stars revolved around the Earth. It’s a pretty safe assumption that if the Ancients believed something, it probably wasn’t true.
Two recent studies relate microbiome diversity to resistance to enteric pathogens.
It is.
And as noted above and in other posts in this thread the gut and the bacteria that inhabit the gut play major roles in regulating health - inflammation, metabolism, so on - in ways that are areas of major research with effects that are local and distant - including on brain receptors.
The … germ … of the concept is quite valid.
The problem is when the woo-meisters go off with the idea in places that the research does not support or even invalidate. When they state as “truth” things that are at best wildly speculative. As also stated above - the problem is not with the concept I’ve quoted, sure involved, even a “starting point,” for some health issues, but with the absolutionist conclusions made that are just dumb.