Meanwhile our economy is designed to require unemployment, so if the government reduced unemployment to zero without any other changes to our economic system it would be highly problematic.

The economy only requires unemployment to keep labor docile and subservient to capital because it is in constant precarity. If the govt offered public service jobs to anyone who wants one it would become the price setter for labor rates and benefits and businesses would have to overbid it to retain a workforce.

That people accept the concept that 3-5% of workers must be involuntarily unemployed to keep the economy stable amazes me. The federal govt doesn't even have to get involved in managing the work which would be better done at a local level. It only has to provide funding and general oversight to avoid fraud and manipulation.