I don't believe that anyone responsible for sending these alerts will be able to send them in anything like as time-critical a manner as you imply - you'll be told that there's a "danger" of a river bursting its banks (perhaps) but not an alert at the time it's about to happen. Just think how long it took them to attempt to send out a generic message yesterday, and even didn't manage to do this.
Which is why I've disabled the thing - it's going to be either too little, too late or it'll be a deluge of useless information about weather warnings because it's over-used.
It's an idea, a bad one in my opinion, which will be implemented poorly.
My view is that I've lived for 61 years without it and I don't need it.
But I can disable it, so that's fine with me.
The test mostly worked well yesterday. Three was the weak link, but it worked for everyone else and that was of course the whole point of doing a test. People on 3G wouldn't have got the message, but as I said above, 3G is being switched off soon and 4G is well over 10 years old now - so I doubt there's anyone with a 3G only phone anymore. The alert even worked on older versions of Android than were stated, which was more a case of 'we can be assured it will work on this or newer'.
iPhone users apparently had quite quiet alerts, so that's another thing to look at. Again, the reason for doing a test and then analysing what worked well, and what didn't.
Networks can easily broadcast a message on local sites, and they are pretty certain of the coverage of each site, so I think it could work very well for things like localised flooding, extreme weather events or even a roaming armed attacker in the area with a warning to go/stay indoors.
Vodafone used to broadcast a code for subscribers to view that showed them what area codes they could call at local rate, and that was in the early 1990s! The tech behind this isn't really that new, albeit the method is different on 4G/5G.