Allow me to preach to the choir for but a moment...
The biggest reason that this is a horrible, horrible idea is that for law abiding citizens large amounts of ammunition is a necessity for safe firearm ownership. Whereas for criminals, it is not.
I'll burn through a couple hundred rounds in an afternoon of shooting. I have to put literally hundreds upon hundreds of rounds through a handgun before I'm proficient with it for self defense (which is necessary for my safety as well as that of others). A criminal has no such need. He's not concerned with accuracy. Hell, he may never even fire the gun he carries. While it may take me hundreds of rounds to prepare for the (hopefully never to come) one round I fire in self defense, he can potentially commit dozens of crimes without ever reloading (assuming he's in it for the money and not a psychopath intent on actually killing people).
It may take him months before he actually has the pull the trigger. He may well end up ditching the gun with the same ammo in it from when he stole it. A single box of 50? Could last him years.
Will this help the cops solve a few crimes? Probably. Will it kick up plenty of false leads as well? Of course it will. Will it impede the training and leisure activities of law abiding gunowners? Likely. Will it impede criminals? Probably not.
Can I get an amen?