Pretty sure it's the kids wanting it done
In this case, almost by definition they can't give informed consent.
Many of the potential effects are impossible to understand as a kid. If you get early puberty blocking drugs, there is no way you can truly understand the risk of reduced or eliminated sexual function 15 years later. For a natal boy, the drugs can prevent genital growth, which is doubly dangerous because it means there isn't enough tissue for the most effective surgeries if that ended up being the plan, and also means reduced or eliminated sexual function if you decide against surgery. And indeed, many trans adults don't want surgery on their functional genitals at all; it shouldn't be assumed they will.
Similarly, it is hard to argue that kids can truly understand the implications of sterilization when that is part of a procedure.
There is also very little research on how the drugs affect the brain.
Although the effects of the hormones are permanent, the claim is always that puberty blockers are reversible. This is the biggest thing that makes me skeptical, because it is clearly a lie. There isn't enough research to come anywhere near saying it is reversible as it is used in these circumstances (the research is on younger children given blockers, not on how it affects people through their teens physically and mentally). Moreover, once you start with puberty blockers, you are virtually guaranteed to continue to the permanent hormones, so the "reversible" claim is disingenuous. On the contrary, it could easily be argued that the puberty blockers put you into a suspended state where you never obtain the ability to give informed consent, because you never learn what you would be risking.
Given that the blatant lie about "reversibility" is present everywhere I look on this subject, it makes it seem likely that kids are also lied to when they are considering starting the procedure.
That said, the argument on the other side is that the benefits (such as potentially preventing suicide, and the effect on adult appearance) are so overwhelming that they outweigh informed consent and all the risks, and that can't be dismissed. It is an impossible dilemma especially with the lack of research.