Except the people have the power to influence that same government through voting, lobbying etc. In the private police hypo, other than money you wouldn't have any power to influence my private police force. Which is why a wealthier individual could take your land, and you would have nothing to say about it.
So if in this "free society", with only private police forces, if an individual could assemble a stronger police force than you can, you will just leave it to faith that the stronger individual will voluntarily honor your private property rights? Criminal trespass occurs every day. But you have faith that it won't occur in your "free society"?