Suppose the pedestrians are walking through the town square. Is that also private property in your world? Do you have to read the Terms & Conditions of the town square, and sign your acceptance, before entering it? What if you own a business on the town square, but reject the rules of whoever owns the road? Do I have to get one drivers licence for when I drive on RoadCompanyA's roads, and another license for RoadCompanyB's roads? Are there road-police checking if people are drunk-driving and checking people's cars when they drive on these private roads, one set of police for each road-owner? I just can't see how road safety could possibly be improved in a libertarian world.
It's expected and encouraged that you will spend all of your time investigating and evaluating the contracts and regulations of countless participants in this 'free society', remaining ever vigilant and aware of the differences and changes to the policies enforced, and be hopeful that as ownership of one domain transfers to another, that the policies won't change. But if they do, you will need to keep abreast of those changes, their new subscription fees, tolls, regulations, and so on.
You will relish the prospects of engaging in all these evaluations and research, being free to make your own decisions at all times, because you will be living the dream of the libertarian society.