Remember, there is a zero sum at play here: to satisfy either half you must apply equal amounts of corrective remediation and get equally unsatisfying results either way.
Um, no. This is NOT "zero-sum". ALL of the children who receive puberty blockers face long-term problems, including emotional and psychological delays.
I swear, this is like the opposite of a LWOP argument. If we were talking about the death penalty right now, your argument is the one analogous to "Use the death penalty more, it doesn't matter if several of the executed people end up being innocent of the crime they were charged with, that's a price I'm willing to pay in order to get the really bad guys gone".
So, you claim emotional and psychological delays. Evidence please? As has been discussed previously offered opinions are inconclusive at best and are offered only for a situation that is not even remotely similar to the context under discussion.
And yes, it is zero sum for all meaningful intents, because the consequences you offer are inconsequential and pale in comparison to the actual things being discussed: surgery.
Because if 100 kids claim trans ideation, and we look at their "destinies", we can pretty well expect about 95-98% of them to actually be trans, creating a fixed pie of outcomes.
This creates 2 outcomes in the "dumbest" formulations of policy (everyone gets blockers for asking; nobody gets blockers for asking), with some graduations resulting in whether filtration efforts are made.
So in this most naive simple no-filter dichotomy, we end up with either 95% of these kids needing surgical correction, or with 5% needing surgical re-correction.
Additionally, for those children forced to undergo an opposed puberty, there are the additional social developmental hurdles of being unable to directly or cleanly access the social groups one is trying to acclimatize to, and being further from the physiological states one needs exposure to to cope with their adult hormones in general.
There are analogical incompatibilities, further, in your formulation. People don't want to die. They DO want to go through the puberty that fits "who they really are". The unilateral imposition against right does not analogically consummate with a unilateral right against imposition.
More "if we let women vote, some will vote against their interests, merely a second vote of their husband, so we can't let any women vote at all!"
I'm willing to accept the consequences, however unlikely if I am wrong, to have the benefits I gain in the likely outcome that I am right. This is standard risk calculus.