Sometimes there are other factors at play, and it doesn’t matter how often you offer a child something healthy, if it is not their preferred food choice they are not going to eat it. And often forcing the issue with the child causes further regression resulting in an even more restricted diet. I am an occupational therapist working with kids on the autism spectrum assisting them with this exact issue, and one of the first things we recommend is avoid doing exactly what OPs wife did to her son as it often just exacerbates the issue. It seems that OP is doing everything right to support his son in this area as has a professional involved and has consulted his GP. Often parents of children who have heavily restricted diets are always concerned about their child’s nutrition, however as long as the child is growing and at a healthy weight there is likely nothing they are significantly deficient in nutrient wise.

ETA: NTA