A website is not the same as having robust infrastructure for public notifications. And to be clear-- neither is twitter, but a website you have to visit isn't as convenient or useful in an emergency where you want people to receive an alert without going to a website.

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.