I don't know what the doctors say, but from experience, I found that when I ran hard the day after pitching a game, things felt better. I would get a real good sweat going and after a shower, my stiffness was gone and my body felt better. The running was no fun, but when it was over I always felt better and would then play some catch.
If I did not run, my body would feel stiff and sore and I would not play catch. When I played, you only had three days between starts and a guy wanted to get his body feeling good as soon as possible, because the 2nd day after your start you would be throwing BP and/or a bullpen.
As far as ice goes, we only used it on an injury. Nobody iced after a game or a bullpen. Koufax was the first guy to use ice after he pitched, and that was because his elbow was injured. After that, some guys started using ice......I think most of them did it hoping they would end up throwing like Koufax.