It wins by a huge margin on the energy to weight ratio. In scenarios where weight doesn't matter it's dumb, but there is potential in places like air travel where it does make sense.
It's mostly landing/takeoff records. Big airports have takeoff and landing fees and would keep records such as this for accounting and legal reasons. Being a major airport like LAX means it's probably mostly private/commercial jets, but also plenty of small time hobbyist aviators are probably wrapped up in this, and would be the only victim here ( general aviation pilots tend to use smaller, local airports but still on occasion hit the big ones).
You apparently haven't tried calling local government agencies in mid-size cities, or a good chunk of airlines. It's frustrating and I welcome anything that can help.
Is there a picture of the phone under the seat?