We do have the same system, commonly used for Amber Alerts, Silver Alerts, Blue Alerts, fires, floods, COVID-19 lockdown, foreign missile tests, etc. However there's no mandatory ack, and except for "presidential alerts" they can all be turned off. That's what I did after I got woken up for an evacuation notice 20 miles away from me, feel back asleep, and got woken up again by the followup message 30 minutes later saying it was just a drill.
Anyways, the wireless emergency alert system has like 5-30s of latency. I suspect that might be enough to make push notifications a better solution. There's a # of apps taking that approach (full disclosure, my employer makes one of them), I think they all ingest data from a private USGS Kafka server