Sorry, Michael, but I believe you are both alarmist and incorrect. I also think it's really arrogant to come into a forum and start spouting random and false advice to women who have already been around the allergy wheel a few times. You probably won't read this, but man did it strike a raw nerve with me this morning.
Tomatoes are actually fairly high on the list of *allergenic* foods, especially in children. They are in the short list with citrus and strawberries after the top 8. Potatoes seem to be regarded to have a relatively low-allergy risk. ETA: link to list
As far as intolerance, I think nightshades are fairly common. They are inflammatory for many people - which is why many people who suffer from arthritis are advised to go on a nightshade-free diet with a pretty good success rate.
Personally, tomatoes were our first OBVIOUS trigger food for DD1. That is, we noticed an immediate correlation to a rash on her face and yucky poop. We've taken them in and out and in and out for almost two years now. This last pass, we've been eating them exclusively cooked or fermented and peeled, cored and seeded. We seemed to be doing okay. DD's eczema was actually clearing for the first time in months and months and months. However, yesterday, I had a bunch of tomatoes to cook and I didn't have the time to peel, core and seed them. We ate them in the form of spaghetti sauce (also had eggplant for the first time yesterday, not good timing, I know...) DD's eczema is flared again, though not as bad as it can get, and she has borderline diarrhea. I consider that a trial of seeds & skin and I regard it as a fail. For now, we're taking all nightshades back out, just as a precaution. She seems to do okay on potatoes, as long as they are peeled. Many people who have sensitivities to tomatoes and/or potatoes have a greater issue with the skin.
Who knows, though... DD2 gets terrible gas from peppers. I think nightshades are just a bad idea all around for our family. Add it to the list. We are now back to the most restrictive we've been exclusive of an TED. Our no list is: dairy, soy, corn, gluten (including special care to avoid x-contamination), tree nuts, peanuts, all legumes actually (including green beans), all seeds, citrus, garlic, turmeric, artificial colors and preservatives, coffee, chocolate, sugar... And now, nightshades. Woo. But, her skin's almost clear and her sleep is better, and that is so worth it.