I would personally prefer to just lose my phone and have robust measures to stop thieves from accessing my data than increase the possibility of bad actors/govt using it as yet another surveillance tool (or at least more than it already is).
Prey (preyproject.com) does this. It'll take pics and screenshots and send them to you along with GPS coordinates at regular intervals.
Edit: Uhh, repetition it seems. God damn I need to not leave HN windows open for a couple hours then replying without refresh.
Obviously if your day-to-day as a police officer involves the cartels or something you won't care about an iPhone. But if you live someplace where a murder would make the news regardless of the circumstances, someone will probably look into it if you can prove you know where the thief is (or that the phone was in a given house/apartment).