This happened a while back in the conversation, but it hasn't really been expanded on, and I have not really been keeping up because of a combination of moving house/unreliable internet/life reasons, so...
Actually, a vastly more accurate and realistic comparison is between Gender Dysphoria, and the underlying disorder that causes (extreme) forms of Anorexia and other forms of self mutilation. There's a clear, obvious, neurological issue that generates a level of self hate. That level of self hate then expresses itself in a variety of ways to hate one's own physical form. Which then evolves into a belief that there's something wrong with the body itself. Believing you're really a pony, or really the incarnation of a dragon, or really a girl instead of a boy... falls into this rather broad sequence of mental illnesses.
This is a tempting comparison to make, but I think it's a mistake to treat it as a 1:1 analogy. First and probably most obviously, people with gender dysphoria who do HRT (hormone replacement therapy) or socially transition generally report a pretty major reduction in their experience of dysphoria. Anorexics who lose a great deal of weight typically still perceive themselves as overweight and desire to lose more weight.
Actually though, there have been some recent studies about eating disorders and proprioception (i.e. the sense that tells you where in space your body is) that suggest that anorexics actually have an inaccurate neurological map of their bodies--they feel like they are taking up more space than they actually are. For instance, in the study I'm thinking of (which I may try to dig up later), lots of anorexics turned sideways, as you do when you're trying to squeeze through a narrow space, even in spaces where they actually had plenty of room to pass.
I've heard it suggested that some forms of gender dysphoria may be caused by a similar disconnect between the body and the brain's map of the body, although I don't think I've read any scientific data supporting it. But I think that it's a mistake to frame all (or even most) dysphoria in terms of a hopeless search for perfection. That may be how some people who experience dysphoria perceive it, but I think it's probably not the underlying cause.
Also, it seems like it is pretty common for people with various types of body dysphoria or dysmorphia to have co-morbid conditions (depression, anxiety, OCD-like symptoms, et cetera), and it's hard to tell which comes first. I mean, lots of people have situationally-affected depression, so it seems likely that constantly feeling like you're in the wrong body would also make you depressed and anxious, but it's hard to eliminate confounding variables here.
... To my knowledge, there has never been an extensive test to see if this method would work on people with Gender Dysphoria. All honest interpretations of the data suggests it likely could and would, to the extent that it works on OCD and other Dysphroria conditions like Anorexia and addiction to plastic surgery (although the treatments are always a bit hit or miss, if we're being honest).
However, the politics of the issue make it fucking impossible to get such a study done. Because some people are obsessed with things that sound pretty, like political correctness, instead of worrying about science, knowledge, and fact.
The problem with this is that the majority of trans people seem to strongly prefer a cure for dysphoria that involves changing their bodies to a cure that involves removing dysphoria without transitioning. Like, the medical world has a finite amount of resources, it seems reasonable not to prioritize treatments that your patients don't want and would avoid. Also, you need to get people to sign up for studies. Studies that give people a treatment that they have not consented to and would be horrified by generally do not get IRB approval. If there were a big population of people with gender dysphoria who were like, "I don't want to transition, I just want to be happy with the body I currently have," then it seems like this would be a reasonable course of study, but if there isn't, then it's...not very useful practically?
(To be fair, it is possible that there is group that fits the above criteria, but that they are more likely to be closeted/less likely to have a formal diagnosis of gender dysphoria. The problem still holds in that you have to
find these people if you want to test whether a treatment is effective.)