This is a very interesting topic. I have disabled my EAS relay system until I get an answer.
As for the laws on use of EAS, it doesn't violate any of them. It isn't a misuse of EAS tones, since these are real alerts, issued by authorities, broadcast for public consumption, and are simply being relayed as-is, without editing or modification. I am not an authority, nor a PEP broadcaster, just an EAS participant; so I do not generate any of my own local alerts, just relay.
Obviously, if I were sending out EAS tones to tell the boys it's time for dinner, or sending zombie apocalypse messages, that would be a gross violation... but I do think weather warnings and AMBER alerts are important public information, and many times, the EAS relay message comes 5-20 minutes sooner than the same message from our cell phone providers. Here in tornado alley, sooner is better. We could get this same information using a NOAA weather alert radio, but that would be one more device for everyone to carry around.
Alerts from the National Weather Service are considered to be re-transmittable for public service. All broadcast stations and cable systems are allowed to re-transmit NOAA weather radio audio, but many don't since it sounds bad on the air.... they have their own announcers/DJs read the weather.
As for identification: My call sign is embedded in the EAS tones as a participating relay, as required by the rules of EAS. Immediately after an alert has been relayed, (and after ANY transmission has been over for 10 minutes) my controller has a synth voice that gives my station ID in English. (For those familiar, I run a CAT-400.)