They wouldn't need to. By default the tower would send along the signatures for the proper local channel(s) and by default the OS would ship with an app that blindly subscribed to those. The difference out of the box would be that the sources were properly authenticated.

For users that wish to configure such things the difference would be that they could select the app of their choice (fixes the terrible UX), select the sources of their choice (not limited to those advertised by the tower), and filter as they pleased (fixes all the false alarms).

I think this is more useful that it might appear at first glance. Consider for example airports where the flexibility could be quite useful during an emergency response. Many venues would benefit from being able to send announcements of varying levels of importance. Nearly all of us walk around with network connected computers on our person yet our systems lack robust support for such basic functionality.

I think it would increase their trust in the phone system if they could, even if they don't use it in practice.