Proper gut function should allow you to tolerate many foods. The lack of tolerance to gluten indicates a compromised gut biome. It is not surprising that you discovered other food intolerances subsequent to gluten.
WAP's Swiss Alpiners had very good health on a hand made, fermented rye bread, goat milk, goat cheese and goat diet. Note the many things they did not eat - refined flour, sugar, HFCS, vegetable oils, transfats just to name a few. Also, no anti-biotics to mess with the gut biome.
This does not indicate that rye is a required nutrient. Please read (google) the post by Dr. Harris on "There are no magical foods". And, for what it's worth, I think white potatoes are pretty nutritious, although it is probably wise to follow traditional practices and peel them.
If we (hominids) survived 2.5 million years without consuming any significant amount of grains (and we did) and were in very good health (we were), then it stands to reason that we do not require cereal grains for good health. We should be able to get what we need by simply eating animals and plants like we have for 2.5 million years. Of course, we can still screw things up with our modern technology, such as antibiotics.
I should also mention that just because we didn't eat something for most of our 2.5 million year history is not sufficient to condemn it, although perhaps it is enough to at least be suspicious. I shun wheat, not because of it's recent introduction into the diet. I shun it because there is good evidence that it causes inflammation, leaky gut and other gut disbiosis. And because I generally feel better without it (less back and joint pain as one example).