I spent time struggling with this issue, too. My conclusion was different from yours.

There is never a reason to treat pre-pubescent minors medically. Whether to medically treat post-pubescent minors should be a decision for the parents in consultation with their doctors -- not the child, and not the state. Parents, while not perfect protectors of their child, are best positioned to balance compassion and responsibility with respect to their child.

Mistakes will happen. Some parents will deny treatment to their child who needs it (Leelah Alcorn), while some might transition their child who doesn't. And even when parents' motivations are good, they can make mistakes.

But the other options are worse. Minors characteristically lack the wisdom and experience to make life-altering decisions on their own, while the state is the worst possible overseer of any individual's private life.

Something that may need to be clarified, simply because it is so often confused: the purpose of medical treatment is not to change anyone's sex. The justification for medical treatment has always been that, in some cases, it is the only therapeutic approach with any consistency in relieving the negative effects of gender dysphoria and increasing quality of life. That's it; no metaphysical assertions are involved.

Now, many trans people themselves do see confirmation of their self-image in medical treatment; but this is simply a private belief. Trans women often believe they are women because it brings meaning to their suffering; that's what beliefs do, for everyone. But that's not why doctors treat them. These things need to be separated in the public mind, because both sides are conflating them, effectively making this a religious war.