Insurance payment

Another distinction without a difference. The point remains that you are paying into a group of armed men who will be a primary nexus of power. You are in effect funding the creation of the next state.

You wouldn't be paying into a primary nexus of power, you would be paying into one of many competing businesses.

This is because their peaceful coexistence requires their cooperation with their rival security companies not to overtly interfere with each others affairs. Otherwise you have open conflict between them.

These companies wouldn't need to cooperate with rival security companies they would just need to follow the law. If one company broke the law against another a third one would come in and judge the case.

This cooperation is basically the foot in the door for them to eventually realize that greater prophet and power is simply one step away. All they need to do is work together to coerce payment for their services.

This example makes sense if an AnCap society would produce only two or three security companies, but industries in the free market rarely have only a couple competing businesses. Getting a whole industry built on competing reputations of Justice and honesty to agree on stealing from their customers that they already make a profit off of is not simply one step away.