The technology that "turns off" the internet is not, in any way, required to run the internet. A router that uses deep packet inspection can process fewer packets than one that simply routes.
When communication networks can be accessed wirelessly, the devices that can block those communications will simply become part of what we understand as standard communication equipment.
When communication networks can be accessed wirelessly, the devices that can block those communications will simply become part of what we understand as standard communication equipment.