I wonder if they could send the messages to certain counties that are actually relevant to the "breaking" news. Geography based sorting of phone numbers to what I assume must be addresses could be a security issue though so not entirely sure. A better solution could be alert settings that would alert for violent crimes/amber alerts/natural disasters(which should never have the option to be disabled) and maybe a downtime period during the night similar to do not disturb mode on iOS devices that only have exceptions for natural disasters. A system that robust would need integration with individual phone manufacturers like airplane mode which has proven to be efficient.
I wonder if folks get amber alerts if they only use satellite based connectivity. I'm willing to be that Apple will have it automatically enabled in iOS 18.