Interesting post. I usually don't ice things. If I recommend ice, it is for pain, not for tissue healing. Anecdotally, A bucket of water and ice seemed to help my ankle sprains recover faster than not icing.
The evidence though is in the favour of not icing...and no anti-inflams...which is why you often see me shrug my shoulders if you ask me if you should take them...I don't 🙂