I wouldn't argue your points above about wealth creation, but somebody has to draw up the contracts for selling the products that are mined, manufactured, or grown. Someone has to account for how much was mined, manufactured, or grown. These roles don't directly create wealth, but they play a vital role in creating wealth.
Some histories I've read indicate that the Egyptians were able to rise as a civilization because they could record who owned how much grain from the rich harvests of the Nile.
And without doctors, the miners, manufacturers, and farmers would die or at least be much less productive.
You are totally missing the point.