One of the obvious reasons for going on the show is that the participants receive expert diagnosis from specialists and the opportunity to try out various treatments, to either cure the illness or at least to alleviate the symptoms.
Additionally, some people who suffer from certain conditions would welcome a greater acceptance from society. They hope that fellow sufferers will gain confidence from watching the programme, and they hope that their own friends and acquaintances will gain a better understanding of their personal suffering through watching the programme.
The series certainly helps some people. Like many boys. I had acne as a teenager. However, I was one of the minority for whom it never seemed to fully clear up and I was still suffering intermittent facial skin problems 40 years later. It was only when I watched one of those programmes that I realised that my problem wasn't actually acne but folliculitis. Since then I've been able to find ways to improve my facial skin, by treating the real cause of the problem.
Chris