Does the loudness of a gun deter its use in the commission of a crime? I think it does, though perhaps only in a handful of cases. Gang violence comes to mind: the gun's loudness gives you away if you're sneaking up on folks, and makes it easier for law enforcement to locate you.
If a gun's loudness sometimes acts as a deterrent, then the availability of this "piece of metal" will reduce/eliminate this deterrent, and consequently increase the probability of the weapon's being used.
If a gun's loudness sometimes acts as a deterrent, then the availability of this "piece of metal" will reduce/eliminate this deterrent, and consequently increase the probability of the weapon's being used.
The same can't be said for ear protection.