What gives them power is the illusion of the ability to unilaterally use deadly force on a whim. No nation has a standing army or security force of sufficient dimension to quash a unilateral uprising through force alone.

Sure, an individual ceasing to believe in the power of a state is a drop in the ocean, and ultimately will not end well for the individual in most cases.

If a mass of individuals, however, cease believing, then the state's power evaporates. Witness every revolution, ever. It's not a question of the people assuming power, rather just the people refusing to grant the state power, en masse.