We have an abnormal amount of "sore shoulders"- Lea, Weatherford and Pigott, sore elbows- Crosswhite and I believe Whitney among others.
Ice is used to decrease inflammation. When you pitch, it obviously puts a lot of strain on the joints and muscle tissue. When you do that, you want to put ice on it ASAP to try to reduce the inflammation as much as possible so that the tissue and joints can heal. If you don't the inflammation stays, and the "trauma" from pitching lingers. If you do that repeatedly, you run the risk of damage. Also after icing, you want to do some stretching because the ice will cause the tendons to shrink some. That should be done at a minimum. Most people have their pitchers do some running as well. Supposedly, we aren't doing that.
What we are supposedly doing is what they do in Japan- like Matsuzaka where the focus is on throwing A LOT.
Also, in all honesty you can't prevent injuries BUT you can do what it takes to reduce the likelihood of them.