I would say the wealthy lobby the government to violate the property rights of others for their own enrichment, more than that they need the state to protect their property rights.

However, you're right that in a state of nature they would be the one's clamoring most for a state.

Undisciplined

econ

Tax the Rich? Not a Good Idea

The state enforces and supports property rights the wealthy. Good luck to the wealthy in a state of anarchy...they will be crying for protection that is not there and running for their lives as their wealth is taken from them by the hordes.
The greatest and most direct beneficiaries of the states monopoly upon the issuance of fiat money are the wealthy.