That's true, though I think people overestimate the power, efficacy and availability of mental health support.
And the main reason I mentioned it is that you're not comparing like with like. Being a woman without breasts in a society where (for some reason) large numbers of women don't appear to have breasts at all is very different to being a woman without breasts in a society where every single woman except you seems to have breasts, it's treated as an intrinsic part of being a woman, and breasts in general are freighted with meaning about femininity and attractiveness and personality and vulnerability and motherliness and comfort and obscenity and danger and matronliness and sexuality and class and age and fertility etc. etc. etc.
Maybe surgery would help the OP specifically, maybe not. But even in cases where the treatment truly is purely about fixing some noticeable physical abnormality to make them look more typical (in the hope this will have beneficial effects on the way they can live their lives), automatically dismissing a treatment as cosmetic and therefore not worth spending taxpayer money on would be short-sighted IMO.
In carefully-assessed circumstances, this kind of treatment can be medically justifiable, even if it's entirely about the way you look. It can improve quality of life, increase functioning, maybe prevent expensive mental and physical illness down the line.
But sometimes it won't help, because the issue is really elsewhere, or it goes wrong, or a lot of other things. I'm really not on the side of "Go OP, go demand your breasts!"
I just think that some posters were being pretty glib and unpleasant to a distressed woman. OP wanted to know how to navigate the NHS system to request surgical treatment for a medically-diagnosed and very visible physical issue, one that she feels is profoundly affecting her quality of life and mental health. What she got was a thread where I feel like the combined effect is a crowd of people berating her as greedy, vain, selfish, shallow, not trying hard enough, on and on.