Public sector employees solely consume wealth generated by private sector employees who generate a profit which in turn generates a tax revenue base from which there is money to employ public servants.
The public sector is a luxury affordable by a successful wealth generating society. Take away the wealth generators and there is no public sector.
This is nonsense as basic economics. A worker doing x-job (e.g. building houses, providing security services) contributes exactly the same wealth to the economy whether s/he is publically or privately employed. Much of the wealth produced by such a work is expropriated in both system.
The same applies to administrators. Assuming for the sake of argument that paper-pushing administration is necessary for society to work, then the work of a civil servant in administering a project is just as wealth generating as the work of a private administrator.
In both cases, a higher amount of the social wealth produced in all the above cases is expropriated by those who are richer.
For example, take the a public servant called a "police officer." His or her value to society is to help contribute to public order. All benefit from this public order, it is true, but the rich benefit more. For it is their *greater* property that is defended.
In a state of nature, the physically young and powerful would simply be able to take wealth from the weak (both the weak poor but also the weak rich, who have more stuff.) In actual society we guard against this intrinsic natural power of the young and strong.
But the split is assessing the difference in contribution of public and private employees is merely one of accounting.