Exactly. The current system which requires trans people to jump through hoops convincing various people that they are 'living as a woman' must heavily enforce the rules of what women are supposed to look and act like.
I've got two trans women friends who I've talked about this with, and they have very different experiences of the hoops.
One friend was told she had to do the whole dresses, heels, and make up thing - which really is not her style - before she had any access to surgical treatment to ease the overwhelming sex dysphoria she experienced or was able to get a GRC, and says that she got zero psychological/psychiatric support for anything she might have needed help with, and found the whole process very distressing.
Another friend said she found the doctors really helpful in challenging what were then her rigid ideas about gender (she says at that point she was almost living two separate lives) and letting her explore her identity and different ways of being, and credits the therapy she had at that point with her being able to live a full and happy life - and she worries that if doctors aren't part of the official process then the NHS will stop providing this therapy to trans people (and people who don't define at trans but have similar issues) who need it.
Obviously that's just conversations I've had and its as much "100s of pms of support" as anything, and other people might have different experiences again (I see MY has written about theirs). Personally, I have a massive distrust of psychiatry (its history of sexism and homophobia, the way it pathologises trauma, the horrendous side effects of some drugs, etc), and I can see that the current process is shit for non-binary people especially. But at the same time, I think that self-definition goes too much the other way - I think the key thing is there has to be some sort of social process and any legal definitions or official process also need to have some kind of basis in the social (and also needs to weed out sex offenders and the like).