That doesn't follow at all and isn't implied by the above model.

Ok, why are we unable to find productive work for the workers?

Lack of ability to find good, regular matches between demand for specific labor services and workers capable of providing such services (sometimes called "sustainable patterns of specialization and trade").

The point is, it's logically and economically possible. You seemed to be under the impression that this situation is inherently contradictory, when it is not.