I wonder how long until rich parents are giving this to their kids who will "only" be 5'10" so they can be 6'2"?
So yes, rich parents are already juicing their kids up on HGH to give them an extra inch or two of height. It's not the same exact treatment as the OP but it is happening today.
https://www.thisamericanlife.org/687/small-things-considered
The problem with giving it to healthy children is that it could make their lives worse even though they get taller (otherwise I see no problem with taking it).