So, the requirements are more than a website, but also not a private 3rd party platform w/o service guarantees, and preferably something that doesn't have municipality, department or agency rolling their own solutions, duplicating effort, etc.
In the US the traditional systems are Emergency Alert & WEA but those don't encompass all the public awareness & notification needs that drive organizations to use something like Twitter. I'm not sure if the right answer is to expand those or creating something similar for scenarios currently outside their scope, but we could do worse than starting the conversation with that question.
The online strategy so far, has to be where the people are, so most governments have multiple social media accounts, like Facebook and Twitter, and also websites and RSS. I’ve also seen, depending on the government, Instagram, TikTok, WhatsApp, etc.
The reality is that when it comes to spreading info to citizens you can lead a horse to water but you can’t make it drink.
In other words, 'website' is visited. Information is accessed and sent back to the requester.
That's not how it works. Unless it's the foreground application, the application is not running; it's not kept open in the background. Instead, what happens is that the application registers with a push notification system when the user first opens it and logs in. When the user should be notified, the website sends a message to the push notification system's central servers, which notifies the phone (the push notification system does stay open in the background, but it's shared by all applications in the phone), which then starts the application on the phone to show the notification.
That said, does it change twitter's status as a website that just happens to have functionality X ( push notifications )?
Well, apart from the app
related content that is identified by a common domain name and published on at least one web server
If that is the case, app is just a bastardized website.
You're evacuating, driving along a highway, and during the course of your trip the available evacuation routes change. A website is useless here.
The context of the conversation is emergency situations, that has to be taken into account when thinking about the required public notification infrastructure.
What Twitter was is better than Facebook, the main other governmental alert platform.
Turns out they used twitter because that's where the users were.