FTR: when I first learned about the puberty blockers, I was already a neuroscience student that had already attended lectures on the neuroanatomy of self-identifying transgender people. And, I will admit, I thought the entire concept of puberty blockers was amazing. I'd never thought of it, and it was a "omg, that's so obviously useful" moment.
You know, a simple calculation (or pair of calculations) would be pretty useful. Instead of everyone 'going by feel' on what feels right, it helps to create an internal metric.
Early on, we use puberty blockers in order to reduce psychological pain in someone experiencing distress. As options are slipping away due to body changes, any presenting dysphoria is going to be aggravated. So, an early metric to watch is "does the cohort receiving treatment experience less suffering?" It's an important question. Now, sometimes we 'force' minors to do things 'for their own good'. And sometimes this is the correct pathway. But sometimes, it works out poorly. That's a later measurement.
Later on, the question would be "what percentage of people perceive that they benefited vs were damaged by the choice they made. Because it's easier to measure the regret of a choice you made (vs. an opportunity lost), the language around these surveys needs to correct for that. So, for example, if 80% of people who didn't get puberty blockers end up experiencing lifelong psychological anguish, but 10% of people who did get blockers truly wish they hadn't, then that would be one sample set. Compare it to the opposite, where 10% of people who don't get them end up experiencing lifelong anguish, but 80% of people who got them 'regret it'. Whether we cared about the psychological pain of the teenagers will be very dependent on those numbers.
And I think it's just important to have a sense where those numbers should be. Everything else is going by feel.
By analogy, the majority of Americans think that foreign aid should be reduced to below 10% of the federal budget. That's how they feel about things. And it's important to have a gist in your head before measuring starts.
As to why the courts would be necessary in the UK, well, that would be a function of judges figuring out that the underlying medical regulations were insufficient. Honestly, I can see that happening. We're still in the early days of treating this condition, and it's not like "psychatric research" is a priority in anybody's spending patterns.