first, silly? hardly. Just because you cant conceptualize it doesnt mean its 'silly', just that your unable to think about it without the bias of having been under a government system all your life, which says more about you than it does the idea.
secondly, private law and security already exist and require no government to manage.
lastly, most of those high prices are due to the way government pays companies to build the roads FOR THEM. By keeping the companies the government contracts with or auctions jobs off to a monopoly on the services, the companies which make materials FOR road building have an interest to make the materials higher cost knowing that the tax payers are footing the bill. Its also why all companies the government partners with in its corporatist system get bailout and subsidies, they have an incentive to produce inferior products at higher costs knowing that they cant go out of business because the government pays to keep the doors open and the lights on.
without government, those prices will decrease to market levels, making it much more cheap and higher quality