If this was only used for *real* emergencies, then you'd be right. Unfortunately, the bar for what constitutes an emergency will be constantly lowered until they're sending out alerts for the most inane crap imaginable.
For example, my wife works for a major university. After 9/11 they decided to create an alert system to keep employees and their loved ones informed in the event of major emergencies. The system was intended for things like terror attacks, earthquakes, tornadoes, alien invasion etc. My wife signed me up so that I'd get a text message when ever they issued an alert. At first, I'd get a text every few months as they periodically tested the system. Then they decided to use the system to warn people about violent crime anywhere near the campus. Then it was power outages. Pretty soon it was building maintenance issues. Now if someone on campus gets a hangnail, I receive a text message keeping me informed. It is indeed fucking moronic.
This NY system will start out the same way, and end up the same way. People will be getting alerts because of a traffic accident half way across the fucking state. People will hate it, and turn it off if they can, thus totally defeating the original purpose. If they can't turn it off, they'll totally ignore it and quickly dismiss the message without reading it, once again totally defeating the original purpose. It's a bad idea. There are plenty of other ways to inform people in the event of an emergency. This is just stupid and will be waste of money and effort.