Secondarily, you should note that my country (the U.S.) is not a democracy; the fact that we have a constitution and checks and balances on a federal level means that it's much more of a republic. The idea of republicanism, with a lowercase r, means that people have supreme power over legislation. Constitutionalism dictates what is legislation and what is foundational (and rarely modifiable) legistation. Hayek in particular advocated for an end to fractional reserve banking, floating exchange rates, and especially the manipulating of central bank interest rates which (along with fiscal policy) to him made "free money" which caused bubbles in the future. Thus, he was not exactly keen on the very changeable nature of democratic economic policy. For that matter, I am too- it is sad to me that many of what I consider integral conventions of economic and political liberties are being curbed for the sake of free stuff from candidates.
This is relatively semantics, and there is argument to be made over whether or not the general public has a genuine voice in the appointment of leaders with corporations, media bias, and other powerful groups influencing the funding and coverage of candidates. But the United States is very much intended to be a democracy.
A representative democracy, to be exact. The general public isn't going to be savvy on the intricacies of financial management, foreign policy, etc, so the idea is to appoint leaders experienced in such things as opposed to putting up a majority vote for every single decision under the sun. The republicanism you describe is also known as direct democracy, which uses a majority vote for legislation.
Sorry to detract, but this is a thing I see when people say "democracy, not republic," in that most of them time it's leveraged by right-wingers to try and distance American ideals from Democrats (democracy) and make it seem like Republicans are closer to it (as in the association with the word "republic"). I don't think you're right-wing in the conservative sense, at least not mostly, but it's a thing I see crop up a lot.
On the privatization of roads, I would argue that this is technically not restriction of movement because of a beautiful thing: sidewalks. Now, you may laugh, but the country is technically walkable. More important, however, is that it is foreseeable that some might not be able to travel if one believes that daily passage tolls on a section of road would be dollar per mile more expensive than taxes for roads; however, roads are not "public goods" in the economic sense that they are neither non-competitive nor non-excludable. Further, one will see that roads are diseconomies of scale, and thus are better off under small companies anyhow.
You can't drive on sidewalks. In the 1950s, the federal government made a major highway program to link the country's roads. This was instrumental not just for land-bound trade and communication, but a great boon for the public as it made it easier for people to go to more States and thus easier to move elsewhere. Before then a cross-country road trip would involve weeks if not months of driving through back roads, unagreeable terrain such as mud and mountain passes, and the like.
Going back, seeing the argument of privatization of roads, security, and other public services by Libertarians is a hard sell in that while some are inefficient and can be done better, they do result in good things on a wide social scale. Many Scandinavians are perfectly fine with high taxes because said taxes are used to fund quality healthcare and education which would be harder to get otherwise. Privatizing roads be a hard sale for a guy like me, in that it would be more work to see if private companies are restricting access or charging higher rates, when as it is now I can just drive my car to work without having to worry about contract negotiation with some corporation to use their roads.
Secondly, I don't care that you've been here for a long time, but at least treating me with some respect would be nice; I'm not attacking you or anyone, I promise. I'm just seeing what people are curious about.
I have yet to peruse the whole thread, but I think the thing is that Elliquiy, has a large liberal or left userbase, and even 'mainstream' Libertarian ideas and their proposals are extreme. In spite of the many wrongs the federal (and even state and local) governments have done, they do provide many important services to many people every day. Gutting them on a large scale will have drastic negative effects on many people, and there are many public services which can't be effectively privatized without prices shooting through the roof because it's very hard to make a profit off of things like mail or waste management.