That certainly is a vast hodgepodge of concepts. For the sake of staying on topic it isn't about what I think or approve of or want for myself. We. The people. WE. Not you. Not me.
If there is a clause somewhere in our Constitution that provides for any of us dictating other people's life choices that do not actually effect us please reference it so we can establish first whether restricting transition procedures is something the government has any say in that would be a good start.
You phrase the question with 'just because someone wants them to' and I would ask should they be told NO 'just because someone does not want them to?"
The law just signed into effect for Texas is a reaction to an issue I would argue was never considered by our founders. But they did lay a framework to help guide us through the process. It does not being with 'No until I say its ok' in order for us to restrict choices and behavior we need to establish a need that outweighs a person's individual liberty.
I do not believe the removal or addition of breasts, or reconstructing dicks into pussies etc adversely affects the ability of the body to function so outside of reproductive potential (which does not define a man or woman) I don't see a medical argument against it. Certainly people have the choice to get a vasectomy or hysterectomy type of procedures to end their ability for reproduction.
The current legality exists for people to choose transitioning and legally becoming a different gender. I don't need to argue for it as again our liberty provides for choices others don't agree with. You have the burden of proof here. An argument of mental illness would need to show the person is some threat to themselves or others and I would argue most people who cross dress or transition are much more a threat in that way when denied their choices.