It would only work if all the privateers get sent to one specific state like Texas and the two systems are kept completely separate.

Let everyone move to Texas and pay no taxes, but every hospital visit or doctors visit is paid out of pocket or by insurance companies, no one has social security or welfare, every road is a toll road, you pay a private fire fighter company a monthly fee to be on their protective detail, police are private security firms you also need to pay a fee for protection or to investigate any thefts from your property, there’s no mayor or other elected representative for their town because where does the money come from to pay them, the army is also a private security company, the list goes on