If every modern society has chosen to have police, I think the burden is on you to prove that every modern society is wrong.

Books are text. There is not actually anything preventing you from conveying the relevant information in an HN comment. Here, I'll do it from the other side.

There is clearly no physical law that says private companies can't hire construction workers to build roads. But private roads are economically inefficient.

Roads cost money to construct but not to use. Road maintenance costs are overwhelmingly dominated by natural forces (i.e. weather). Therefore the efficient price for road use is a fixed cost of construction/maintenance and ~$0 per mile.

But the typical private solution to paying for roads is tolls. Tolls don't match the efficient cost structure. They convert sunk costs into variable costs which inefficiently reduces usage of the valuable resource. This error compounds itself. If covering construction/maintenance costs would cost $.25/mile but that price deters some usage, then the price has to be raised to meet total costs against the lower usage, so the price goes to $.40/mile. That would deter yet more usage which increases the price to $.50/mile. The price stabilizes at quite a high price point that deters a large amount of productive use of the roads.

Another problem with tolls is that they don't match the value received from the resource. Someone who doesn't drive at all but once had to have an ambulance take them to the hospital will have derived the full value of the rest of their life from having the roads but will have paid hardly anything, which puts higher costs on everyone else and further compounds the inefficiency above. In a less extreme example, someone who ships a small quantity of high value freight over the roads is receiving the same value from them as someone who ships a large quantity of low value freight, but is paying significantly less.

So tolls are terrible, but what says a private group can't build roads and then charge a fixed annual cost to local residents for access to them? That actually works perfectly well, except that it's irresistibly coercive. Government-level coercive. Either you pay the "road tax" or you aren't allowed to leave your house and no one can visit you or deliver anything to you. It works for exactly the same reasons and in the same ways that government roads work because that's effectively what it is. The taxing power is derived from a monopoly on travel rather than a monopoly on force, but travel is important enough to make that a distinction without difference.

Now you've got a counterargument to make. The road company could have competitors. If they're doing a crappy job then someone else can build different roads and people will sign up for the other one. It would have to be a really, really crappy job because it would have to justify the cost of a second road network, but in theory it's possible, right? But not in practice. The "tax local residents for access to the roads" model is the most efficient one because it most accurately tracks the operator's actual costs. If someone is operating under that model, they're going to win in the market against someone who isn't. They're going to capture every customer whose road usage if charged per mile would put them over the fixed annual cost. But the per-mile competitor still has the same fixed costs, so for every switching customer they then have to increase the per-mile price, while the annual-price competitor can lower the annual price. In every iteration, the heaviest using customers who still use the per-mile roads realize that the new per-mile price puts them over the annual price, switch to the annual price company and cause another iteration, until the annual price company has 100% of the customers. Because their pricing model is more efficient.

So OK, both competitors can charge a fixed annual price, right? And then the same thing happens but the advantage goes to the one with more customers to start with. They have the same costs but more customers to amortize them over so they can charge lower prices and the lower prices attract more customers, creating a feedback loop that destroys the competitor. Or, if the competitors are willing to set prices that won't allow them to recover their maintenance costs, it creates a price war that, again, destroys one of the competitors (whichever one has the smallest cash reserves) and reinstates the monopoly. Which is why roads are a natural monopoly.

So the only efficient way to have "private roads" is to have a monopoly road company that collects periodic "road fees" from basically everyone regardless of how much they use the roads. But it's still a monopoly and monopolies can be very abusive if unchecked. So maybe what we need to prevent that is to make sure the local residents own the company, so they get a vote in how their road fees are used and how the roads are maintained. Do you see where this is going?