The problem with shutting down the internet and cell phones is that so much of emergency services today rely on them. They cant shut them off without cutting off their own help.

There’s so much that goes on that you don’t want hitting scannerland that a great deal of LE work is done by phone rather than radios. That will not change in an emergency, it will probably multiply because of all the radio traffic that will be happening.
Reports and computer aided dispatching are done in the patrol cars, via the internet.

What generally happens is the power to the towers is interrupted and service is lost.