Let me throw this out there.
If your teaching this to hitters who push the hands and have nothing close to bat drag. hand pushers because they make it farther in the game then bat draggers. Then does the supinate TTB mechanics work fine for them?
Great point
I have kids that swing down works for them
I have kids that swing up works for them. Its up to me to monitor it
If you have a pushy kid and saying supinate the top hand works to get them to use the hands as a pivot and to keep them from pushing forward..Have at it. Personally I don't use the term supinate commonly either.
My point is for most ...the though of launching rearward and top hand working first is a bad teach!