Ignoring the weird philosophical overtones that come with any libertarian treatise on economics, the fundamental reason why we should eliminate involuntary unemployment is because it is the imposition of taxes to provision government which creates unemployment in the first place.

It doesn't really matter if workers in a job guarantee program are productive in the sense of being profitable, because involuntary unemployment has a negative (not neutral) impact on productivity at an individual and a societal level.

Ensuring spending is at full employment levels through a job guarantee maintains a buffer stock of employed and employable labour, ready for work in either the public or private sector, or at the very least prevents intergenerational poverty cycles from forming due to the negative impacts of involuntary unemployment.