It seems quite biased to claim the private sector is the only provider of goods and services in a society. In my home country the provide quite a lot of services: health care, education, child care, police, fire fighters etc.
And to be pedantic, the Soviet Union is an example of the ability to provide good and services entirely without a private sector.
Even in Norway the public sector has its own incomes. It does not rely exclusively on taxes as e.g. the Norwegian government has a vast soverign wealth fund, and ownership in a number of companies bringing in profits.
A mixed economy like China has substantial amount of public sector companies.