Having a c-section might not be the underlying cause of the problem. Doctors carry out c-sections when a vaginal birth would create complications for the mother or the child. I.E. the mother or child was already "sicker" prior to the c-section.

I'd love to see a randomized control trial for this. To do it ethically, the trial could be designed like the CRASH trials. In those trials, doctors received patients with head injury and administered a placebo or corticosteroids. Since it was unclear whether corticosteroids helped or hurt, it was ethical for doctors to randomize patients. For births, only situations where it's 50/50 between a c-section and vaginal birth would qualify. Perhaps it's too small a subset to be workable or perhaps it's never 50/50, but that type of trial would provide much stronger evidence for this intriguing idea.

On a personal note, I was a c-section baby and seem OK!