I definitely agree with you on this one.
But that's where I feel the line gets super blurry. This is not a white or black issue. Gender Dysphoria is an actual documented mental disorder.
Feeling ugly (or in the context of this debate, being classified as ugly), in general, it's not.
Body dysorphic disorder is a real thing (probably spelled incorrectly). There are people out there that feel like their limb isn't theirs - it is alien - and go to great lengths to stop it. Some folks spend lots of time and money hiding "flaws" (like their nose), even when they cannot really afford the costs every month, and avoid dating and going out because of these things. Just because it isn't a specific disorder doesn't mean the people are healthy.
And then there is another category altogether: Folks that have had accidents of different sorts. Sure, facial scars from burns or a disfigured nose might not actually cause a psychological disorder and it might not make things physically difficult, but damn it is hard to argue that fixing these things (when possible) wouldn't improve one's quality of life.
Or perhaps a mental disorder in those other people, but that's not likely.
On the other hand, your health insurance could easily create subjective definitions to deny coverage. Because unlike gender dysphoria, beauty is not binary.
With Gender Dysphoria there is only one direction when it comes to re-assignment options, and it is fully documented that this surgery is beneficial for the patient's mental health.
With beauty/ugliness, there are hundreds of possible permutations and no documented precedence to validate that this is a necessary surgery.
If someone's nose is causing as much distress as gender dysphoria, why not?
Sex reassignment surgery isn't easy to get, and presumably coverage for "corrective" cosmetic surgery would also take some evidence. Patients couldn't just make an appointment on a whim.