I'm a really small person with a really big chest (E cup) and getting rid of that is what's most important for me. My chest impacts hugely on my life. I have really low blood pressure, so getting too hot (I live in Australia, so that's always a problem) can make me pass out, it can happen up to 10 or more times a day, and having to wear a binder makes that problem so much worse. Not to mention I have problems with the cartilage around my ribs, which makes breathing hard enough as it is. And from a passing point of view, no binder gets me flat. Because I have such a small frame and large chest, it's always visible no matter what I do.
The first psychiatrist I went to was a total cow, but even she could tell it was a big issue for me. She wrote in her letter to my endo that while she thought HRT was a bad idea, because it was irreversible and I was still young, that chest surgery should be considered for me. I don't see how chest surgery is any less permanent than HRT, but that's beside the point. You could probably get a therapist to write a letter for surgery without having to be on HRT, so long as you explain yourself properly.
That being said, practicality dictates I go on hormones first, since I won't be able to afford surgery for a
very long time.