You see what you want to see. I see the courts interfering with what should be a parental decision. If she still wants to change genders when she reaches legal age and can pay for it herself then let her have at it. Next some court might decide what church you must send your kids to. Think of the larger implications than just one kid.
The mother approves, as the parent has to because he's under 16. Considering the mother has custody (which says more about the father than just an objection to their son being who he is)...
The issue with 'waiting' is that, as Trans, blockers are pretty much useless once someone's older, and for Trans women especially, passing is one of the bigger issues. Trans men do pass easier than Trans women past puberty. With blockers in place until HRT can truly start, Trans women don't develop the more visible male characteristics which increases their likelihood that the dysphoria won't be so bad later in life.