What about satellite phones? Or 'ham radio', or even e-mail? There is no reason to suppose that the bomb, if quite powerful, could not be connected to the old fashioned wired network.
As for the question: "why is such a powerful tool designed so poorly that simply knowing its broad details would enable someone to undermine it?"
When the mathematician Kurt Godel was being inducted into USA citizenship, the presiding officer welcomed him noting that he was fleeing from a dictatorial regime to a country which could never be a dictatorship. Godel rose and stated that having studied the US Constitution, he could state exactly how the USA could become a dictatorship. (Godel's supporters told him to 'shut up'.) I have rarely come across political procedues which were both sound and complete (in the mathematical logic sense of the terms), so don't expect '303 to be.
The real question neither side has raised is how they judge whether more lives will be a risk of harm with or without the cellphone signals. They can be used to summon emergency services to fires, critically injured people, or crimes in progress (I did), of which use I presume the forces of law and order would approve.