You're describing a post scarcity world. The whole point of an economy is to manage scarcity, talking about economic value post AGI is nonsensical. The responsibility to produce and distribute goods post AGI will fall to the government. Your doomsday scenario only exists in a world where the government purposefully chooses to deprive its citizens.

People who don't want to depend on the government could always spin up their own AGI and become self sufficient. Some solar panels, a few robots and some farmable land are probably all you need when it comes down to it.