I am a layperson but I would hope that if medical professionals were going to prescribe a drug treatment which they know will have a significant effect on a child's development they would do everything in their power first of all to try to look at what might happen both if they do and don't prescribe it.
In the case of PBs, they have research to consider on how PBs affect children given them for precocious puberty. Are children given PBs for gender dysphoria put on the same dose? Do they take PBs for a longer or shorter time? I assume they start them much later than children suffering from PP. Does that affect how they work?
What happens in normal puberty? There must be research about that, and about all sorts of conditions known and studied where something has gone wrong.
Break it down as much as possible. One detailed list of changes that normally happen in female bodies during puberty, another for male bodies. Which of these would be affected by PBs? If the PBs are stopped, does the process that was halted/prevented get going again? Does it happen as you would normally expect if no PBs have been taken? How important is the change?
Set against all of this the outcomes for children with gender dysphoria who have not had any hormone treatment. Separate out those who got no help or support at all from those who got counselling/therapy/psychiatric drugs for depression, anxiety etc. Make sure you look at girls and boys separately. Look at co-morbid conditions. E.g. how does a child on the autism spectrum disorder cope with puberty where there are no gender issues?
Having done all of that, specialist clinicians could have an informed debate to decide whether the problems resulting from taking PBs are all outweighed by the problems from not taking them.
I genuinely have no idea how much of this work has been done. I have the impression that research in this area has been limited because of fear of claims of transphobia, bigotry etc etc. Also, the numbers of children involved have increased hugely in the last 20 years - have the characteristics of the group changed? Is the older research still relevant?
James Caspian at Bath Spa University was prevented from doing research into detransitioners. Have there been others?