I thought this was a very pertinent point. While I agree that the current market infrastructure would not allow for full unemployment as the situation stands, I would argue that a complete change to a command based economy isn’t necessary either.

The labor market now picks and chooses the (theoretically) most qualified applicants from the pool of unemployed. What is needed to accomplish full employment is a centrally commanded organization, as James suggested. However, that organization only needs to work from the bottom up instead of controlling the entirety of the labor supply. In other words, they would continue hire the least qualified applicants from the unemployed pool until there were no more unemployed leaving the most qualified individuals to the market. This approach would strictly create full employment (0% unemployment). Naturally, there is still the problem of underemployment, but 0% unemployment and some degree of unemployment is still preferable than having unemployment.

See any of the papers on Government as the Employer of Last Resort for more information.