The left believes that a large public sector is needed to achieve full employment. Right-wingers have an objection. Should those who work in the private sector support those in the public sector? This reasoning is based on the fact that the public sector would be useless to the private sector. It also touches on the idea of who is society for?
If society exists for the citizens and not just Big Capital, the public sector is also needed to create full employment and decent incomes for everyone. The right-wing economist Friedman has admitted that the private sector does not want full employment, as capital needs a shirt stock of unemployed in reserve so that the workers and the unemployed become desperate enough not to ask for good conditions and wages.
If you mean that it is creating a hobby for the unemployed to hire them in the public sector, then isn't it an even bigger waste to just keep them completely unemployed without them doing any good except looking for jobs that don't exist?
Then the public is in many ways beneficial to the private. The public sector is what makes a nation's business competitive in technology and drug development. Such development is too expensive for companies to pay for on their own. Profits would also fall in other ways without the public sector. Too many would not have the money to or too little money to be able to keep up consumption with their low purchasing power.
In addition, care rehabilitates the workforce so that it can work again. It creates roads for the company's trucks and cars to travel on. It creates a well-educated workforce that can take on more advanced jobs that, with their increased value added, can be far more efficient than a manual laborer can be. Well-educated labor therefore creates greater production for capital than otherwise. The public sector is needed to create enough cheap housing so that people can afford and have the opportunity to move to where the jobs are.
Environmental scientists have figured out that welfare is also good for the environment.
Without the public sector, more and more people would become criminals when they themselves became ill or unemployed. People of working age would rebel when their parents were left to die in poverty as there was no elderly care.
Already today, a large part of the workforce, especially the female workforce, fully or partially reduces working hours because their parents do not receive any care for the elderly. This reduces both productivity and consumption in society.
The public sector is also needed for the capital.