People will pay for that which represents value. I would insure my home with an insurance company that had a nationwide emergency service offering police protection, disaster and medical response teams. I would insure with the best company but not at any price. It would be the company who offered the best balance between service and price.
It is not inconceivable that these insurance companies would, maybe jointly cooperating, expand their emergency services to include a form of 'home-defence' military. If that was a real concern to people would the majority not see a value? What is the faster at meaningfully reacting to new challenges: the public sector or the private sector?
From the insurance company's perspective it may be they find a strong demand for insurance cover to compensate against the threat of invasion, subsequent loss and damage. Now, if there were enough policies up for grabs, would it not be economic to invest in protection from the threat occurring?
So some folk then think they will not bother with insurance offering cover against war. Good luck to them - in the event of an attack they will be the ones pushing the handcarts full of all they own.
On the whole I think of the entire idea of a stateless society being racked with war as being absolutely improbable since, so far in the whole history of humanity, it has only been the state that has waged actual war and against another state too.
I think a stateless society would become, rapidly, so successful that any other remaining state's populations, or leaders even, would see the results of the model as desirable but imposable to takeover by war because, to capture a prosperous nation, you have to have a nation to take over - with a state to tax the people and so gather the tithe.
A stateless society is by definition not actually a 'nation' at all. Just a lump of land upon which people muddle along the best they can and coexist within their own independently developed and codified rule of law.
If you tell a lie big enough and keep repeating it, people will eventually come to believe it. The lie can be maintained only for such time as the State can shield the people from the political, economic and/or military consequences of the lie. It thus becomes vitally important for the State to use all of its powers to repress dissent, for the truth is the mortal enemy of the lie, and thus by extension, the truth is the greatest enemy of the State.