Cell systems still have the ability to push out a message regardless of how "overwhelmed" the towers are. They'll just drop service to some customers while the higher priority emergency message is broadcasted out.
A cell network doing a one-way broadcast text message to all clients is a solved problem. And honestly, I greatly prefer this way to push out an emergency message than assume I'm tuned to a radio station or broadcast TV, two things I'm rarely doing. I'm way more likely to be listening or watching local or streaming media instead of watching broadcast TV. Or even just not be doing any of that at all. Lots of people I know wouldn't even be able to tune into a broadcast TV or FM radio station outside of their cars.
A cell network doing a one-way broadcast text message to all clients is a solved problem. And honestly, I greatly prefer this way to push out an emergency message than assume I'm tuned to a radio station or broadcast TV, two things I'm rarely doing. I'm way more likely to be listening or watching local or streaming media instead of watching broadcast TV. Or even just not be doing any of that at all. Lots of people I know wouldn't even be able to tune into a broadcast TV or FM radio station outside of their cars.