Yes, I argued the same thing. It's only logical to search for alternatives when system is unable to help or exhibits dysfunctional responses to one's health problem.
At first you go to the GP. At some point you realize that you don't feel understood or taken seriously. Once you've overcome the self-doubt that this can create, you decide that the problem is the doctor, and not you. So you go to the next doctor, who has a different take on the problem and for a while there is some hope that this will finally be the answer. But it's not. If that doctor can't help, then maybe someone else can, after all some diagnoses are difficult to make... it's just a question of getting everything ruled out, right?
Proponents of functional disorders would call this "doctor shopping" but it's normal behaviour. Patients who have particularly bad experiences may end up further on the fringes of medicine than others in their search for answers.
A systemic factor that promotes doctor shopping is that in order to receive support (accomodations, financial support, etc.) you need a diagnosis... so not only does a diagnosis feel like a goal that might lead to a treatment or a cure, but also something that you need just to make life with the illness a little bit better
Patients with poorly understood health problems need a person within the healthcare system they can trust, that can give sensible advice and will not act dismissively. The functional disorder people are trying to position themselves to be that person but they keep failing to earn the patient community's trust because their psychologizing is nothing more than a dysfunctional response.
That trustworthy person will also need to be able to speak frankly to the patient and help them get to terms with an extremely unpleasant reality: that the disease is not diagnosable and not treatable and the future is uncertain. Some doctors may be that kind of trustworthy person, but many are not.
I think most doctors are unable to have this talk and that's why they tend to like the psychosomatic paradigm that belittles the illness, deresponsibilizes them and paints a rosy picture that sadly in the end turns out to be an illusion.