It’s a matter of ignorance and lack of education. I appreciate that you are trying to learn more about this subject, but I feel like there are still a lot of misconceptions.
For one thing, if a medical professional referred to me as an “XY large gamete” person with gender dysphoria, it might technically be true (although not necessarily, since many trans people are also intersex and they would be assuming a lot by referring to someone that way without knowing their medical history), but I would not be their patient for long. Reducing a patient to their genitals and reproductive organs is not good bedside manner. If I were a cis woman and someone called me a “XX large gamete woman,” I would be insensed, especially when very little health care directly relates to my reproductive organs (or lack thereof).
99% of the time, my being transgender has nothing to do with what my doctor is treating me for. My last appointment, the only time she mentioned anything having to do with my being transgender was when she mentioned that, this being a full physical, she would order a full panel of tests, including my hormone levels. We spent 10 times as much time talking about management of my diabetes.
I also feel like use of this kind of language by health professionals occurs as part of an attempt to sound authoritative. You could call a transgender woman a transgender woman (or just a woman). Using specialized terminology from biology might sound professional and precise, but it’s not. And it’s meaningless — if I was XX (and I don’t know what my karaotype is, but I would not be the first XX person assigned male), but had “small gametes,” very little, if any, of my treatment would change.
Sex organs and genitals are really one small part of what we are. So, unless the complaint has something to do with my sexual organs, then it’s irrelevant. Even the endocrinology issues of being on hormones and having diabetes don’t come up much after I have managed my levels for each.