Doing HRT carries massive life long side effects, which doctors are required to inform patients about. In some places, it requires months of therapy and a doctor's signoff. While I'm sure there are people who have hormonal imbalances, and some of them have perceived gender dysphoria because of it, I find it very unlikely (or at least extremely uncommon) those people would then start taking hormones, given that you have to be _pretty sure_ you're trans before getting near hormones. It seems very unlikely that in the course of a dip in hormone levels where dysphoria was sudden the course of action would be to transition rather than to seek an endocrinologist for answers. If this were common, I would think detransition rates, which many studies have shown to be very low, would be far higher than they are.
Even with 15 years of gender dysphoria, it took me six months post coming out to feel ready to start the hormone conversation, and an additional three months with the prescription sitting in my cabinet before I was ready to actually start taking it. Like I said, my hormonal level baselines were normal for a male.
Edit, RE your edit:
> "hormones have nothing to do with it but write me an Rx to mess with my hormones so that I'm more of a girl."
"Mess with my hormones" is a flippant and inaccurate way to describe a very difficult conversation trans people have with their doctors. You don't start hormones for fun and you don't start them because you're high on estrogen or testosterone. Hormones also don't make you "more of a girl." If you are a trans woman, you are a woman, regardless of whether you are on hormones, have had any kind of sex altering surgery, or have socially transitioned. You take hormones to bring your inward sense of identity outward and reduce the pain that comes from your sense of self not aligning with your appearance and the societal demands and expectations of your behavior.