Germany has been doing these or a while now, works quite good (the tests at least). It only works when your phone is connected to a cell tower, though, that's not really a problem over here in Germany but it could be quite a big one in Australia.

I don't think cell coverage isn't that good in the Outback, even with Vodafone doubling their network coverage (har har).

The US has a similar alert system for emergencies and most alerts you see are to look for a number plate because of a recent child abduction:

https://en.wikipedia.org/wiki/Wireless_Emergency_Alerts

Relevant passages:

There are two levels of alert. The “critical” warning for imminent threat to life, like when a cyclone is about to hit, sounds an alarm and triggers a message on a phone’s home screen. These warnings are compulsory and cannot be turned off.

“Priority” alerts are issued when there is not an immediate threat to life but when people are advised to follow instructions before an approaching emergency, like a bushfire designated at the “watch and act” level. Phones can be set to opt out of priority alerts.

Prior to the national test on July 27, an alert will be sent to nine locations in June, including Majura in the ACT, Launceston in Tasmania, Port Douglas in Queensland, Liverpool in NSW, Tennant Creek in the Northern Territory, Geelong in Victoria, Goomalling in Western Australia, Port Lincoln in South Australia and Queanbeyan in NSW.

The test message will read: “This is a TEST alert of AusAlert, Australia’s new emergency warning system. NO ACTION IS REQUIRED. In an actual emergency, follow the instructions in the alert to keep yourself and others safe. Visit www.ausalert.gov.au for more information. This message is authorised by the Australian Government.”

Does the siren sound override a phone set to mute?