I agree that under most English based legal systems, children are highly unlikely to be able to consent to taking puberty blockers. But, I would point out that the same thing is true for many other medical procedures and treatments that children battle. For example, a child may need chemotherapy for cancer. The child cannot consent to that, because of the child's minority status. But, children with cancer get medical treatment all the time. Medically necessary treatment for minors occurs without the need for their consent (which legally they don't have the capacity to give). Doctors and parents perform all sorts of treatments on minors without seeking the minor's consent, but surely the consent of the minor (or lack thereof) would not prevent such treatment if it was medically advised and consented to by the parents. In fact, I would think refusal to reasonably consent could be grounds for neglect.
Puberty blockers could well be life saving, necessary treatment in some cases. The lack of capacity to consent to treatment should not be a suicide pact.