Another objection to GPS is that in less than ideal conditions it's only accurate to plus or minus 5-15m, or even worse (40m) indoors with a poor antenna*. You can't get a search warrant without a specific address, and knocking on ALL the doors of the flats in the worst estate you can think of might not be a survival tactic.
A dumb beacon in addition might give a local fix, but power requirements would probably make the battery large- I've done transmitters that last oover a year on a PP3, but that was transmitting a tiny burst every minute or so.