While I 1000% agree that people should have access to gender affirming care, I don't know that this argument is as much of a slam dunk as it's presenting itself to be.
While there's certainly a contingent of people who want to ban or restrict access to gender affirming care to adults, a plurality of the debate is around access for minors. And minors aren't allowed to get full body tattoos, even with parental consent.
And second, one big distinction is that your insurance company isn't going to pay for you to get a full body tattoo. That's coming out of your own pocket. My understanding is that most of the checks like getting therapist notes are to prove that it's a "medically necessary" procedure. Not defending insurance companies, but when a third party is paying for something there should be some expectation of increased scrutiny on it.
Again, none of that should be interpreted as me saying anything close to "gender affirming care bad." I think people should have access to the care that they need. I'm just pointing out the argument in the OP is a a bit of a straw man.