In the UK we recently had a test of the emergency alert system. Most people had an alarm and a message on screen, with phones locked. There were a few incidents of motorists ending up in road traffic accidents in the immediate aftermath, and some phones reportedly spoke the announcement rather than just beep loudly.

Since the 'beep' is just an audio file, my hunch is that some A/B testing was going on, with most people getting the 'beep' and some getting the message read out.

I imagine that broadcast capability is fully built in, so that mobile phones can replace what we had in the olden days when the government could take over the TV and radio to broadcast whatever they thought was important. I can't remember the last time that the U.S. President spoke to the people in this way, but it used to be fairly common.

I don't think that calling every phone is plausible. In a competitive telecoms market, no provider would build that out. Instead they would keep capacity just above what they know is needed on a daily basis.