You'd probably have to make sure that it only activates if the phone is actually stolen, not just lost. I found an iPad in the street once, took it home, found the owner's details and took them to come pick it up (turns out it was some sort of sale team, and one of their staff put it down and forgot to pick it back up).

I'd've been _extremely_ unimpressed if the device suddenly started proclaiming it was stolen.

To much power consumption when the phone would likely be already out of the public. But certainly an option

Could just phone the police, "Hello I'm an iphone, I am being stolen, my GPS coordinates are ..., and here's a photo of the face of the thief"

Or it could just shock the person holding it until they drop it and run away http://youtu.be/tMa-lwxXWjY

On a serious note, none of these options seem desirable if the Apple account is compromised.

Maybe a good Apple Watch use case. As soon as the phone is stolen from you you can activate the alarm using your watch and now the thief is running down the street with an iPhone screaming that it's stolen. I'm guessing they would dump it because they won't get far before a cop hears it if.