OK, they could do that and break any use of the Internet that is not the Web. I mean, hotels and coffee shops do it until you’ve officially signed up for their WiFi, so your ISP could, in theory, do it.
The obvious problem is that it could easily cause problems even worse than someone not being properly alerted to an impending disaster.
The fire alarm went off in the building where I work last week and everyone ignored it until someone came around telling everyone to get out. We didn’t even know it was the fire alarm, let alone know that it wasn’t a test. The only siren I heard was coming from the server room, and I assumed it was some sort of alert that something had gone wrong with something in there, requiring attention. You could only hear the sirens from certain parts of the building. Many of the sirens didn’t go off at all.
AFAIK nobody was ever told what the reason was that the alarm went off in the first place, other than being told that it was NOT a test. We all just milled around outside for about 10 minutes chatting while three different campus police cars came and officers went inside… eventually we were told we could go back in.
I generally ignore alarms that I hear, because I assume they’re drills or that they don’t apply to me. Bad habit, I know.