I think there is some nuance to that, and IMHO it largely depends on the model of healthcare we are talking about.

In the case of paying out of pocket for treatment, all that's needed is informed consent. E.g. you see an endo, they inform you of the process and all effects, desirable or otherwise. They cannot bar you from treatment, nor are they responsible if the treatment turns out not to be right for you. Once consent is provided, they are responsible for monitoring your hormone levels and adjusting the dosing if needed.

When it comes to socialised medicine, gatekeeping is inevitable. This is for the same reason that someone whose teeth are ever so slightly crooked, to an extent that is only noticeable under close inspection and has no oral/jaw problems, would not be entitled to braces/invisalign. It isn't a medical need, and that person is free to pursue that privately. Attitudes towards gender and transitioning have changed over the years, and there are people these days for whom HRT is an aesthetic choice/body mod (and is partly why I distinguish by describing myself as 'transsexual'). Power to them, but I would not claim that cases like this are the best use of tax revenue. This is where the tattoo analogy has a bit of weight to it.

tl;dr medically necessary for some, and just a form of self-expression for others. That difference can matter to the taxpayer.