I missed this response apologies for late reply:
Also sorry but I will be disagreeing with your assessment as well.
Pediatric endocrinologists give puberty blockers in the form of aromatize inhibitors which do indeed inhibit estrogen production but often they also include growth hormone. Growth hormone given while growth plates are open can and does cause growth in height. The idea that this only works on children with a growth hormone deficiency is incorrect. I'm not sure how that belief got started but it's wrong. The response may be better in those with a deficiency but that's not what we are talking about here.
"Increases in growth and height induced by therapy and improved psychological adaptation
Only one controlled trial has examined the behavior of short children who were not deficient in growth hormone but had been treated with it.
15 Participants were 12 to 13 years old at the time of follow up. After 5 years of growth hormone treatment, 15 children (of 21 who had started) remained in the clinical trial. This group increased in relative height from 2.4 standard deviations below the mean at the start of the trial to 1.2 standard deviations below the mean at follow up. The average height of the 13 short children who had been randomly assigned to receive no treatment remained virtually the same (changing from 2.5 standard deviations below the mean at the start to 2.4 standard deviations at follow up).
That's significant brother especially to a person of short stature.
www.ncbi.nlm.nih.gov