Well, the most obvious problem you fail to see is how to you propose to field a military, and compel everyone who "uses" it to pay up? Without threat of violence, don't you think there will be free riders? Alternatively, you can forgo a military, and be annexed by a neighbor who has one. Assuming you have anything worth annexing.
Crime will still happen, so do we all need private security?What if you can't afford it? What if you have a fire but can't afford...