I think the OP was not so much about icing or heat to promote healing as much as the OP was appalled that any 11 year old could have used his body in such a way as to require therapy of any kind from use of their arm. I am with TRhit on this one. "Kids today do not throw enough"!
My sons would throw with each other on a daily basis, including long toss, a couple times a week. Their arms did get tired, and back then it was all about ice, no controversy back then. But the point is they threw and they had muscle pain, maybe tendon pain, who knows. They iced, rested then threw again. My son at 25 still has a strong arm that rarely aches.
He threw a lot every day or so from the time he was 7 or 8.
It is what it is, a ball player will use his arm and will experience discomfort, even at 11.