This argument seems to imply that if you had a big red button that would uniformly distribute all the world's resources, that we would be stuck in a steady stat

This argument seems to imply that if you had a big red button that would uniformly distribute all the world's resources, that we would be stuck in a steady state and unable to produce anything. This conclusion is obviously false, and I think if you work backwards you can probably find where the analogy breaks down.