The people that own them don't really care that much, because they get their money just the same, and since they have a monopoly, they don't have any real competition unless you take the train or a plane, which simply isn't possible in many cases.
You may currently be spending more than $1400 to the government to pay for government roads. With competitive incentives in road placement and size, you might save more than enough time to offset the transaction costs.
Roads are a high-fixed-cost-low-variable-cost industry. I posted on these at Reddit - http://reddit.com/info/2fquz/comments/c2fttk. Everything that's wrong with airlines will go wrong with roads, and more. I suspect that you'll see massive overinvestment in roads as road companies try to capture market share, then the huge number of intersections (all toll, remember?) will reduce driving efficiency.
Free markets solve a lot of things, but they don't solve everything. There's no magic wand that makes them more efficient than a public solution. There are, however, a series of incentives and information-transmission mechanisms that usually give a free-market operator an information advantage over a public operator, hence letting them produce more efficiently. If the incentives point in the wrong direction, though, you get less efficient production.
Similarly for another high fixed cost industry which you cite - telecommunications.
Free markets might not solve everything, but they're almost always better than the alternatives. As examples of the alternatives, consider the postal service, government-run schools, Medicare and welfare.
Another option is a monthly subscription fee for unlimited access to all roads a company owns. If there are a small number of large companies this might be convenient. And don't complain about fear of monopoly -- the alternative is a total government monopoly.
There are various possible ways the road use for subscribers only might be enforced. Offhand, none sound especially convenient. But they all sound better than the status quo: all people in the area are counted as "subscribers", even if they don't own a car, and are all billed, and this is backed up with guns. That's worse than any of the non-ideal enforcement mechanisms I can imagine. And while it may save a bit on transaction costs, it does that by not even trying to differentiate a subscriber from a non-subscriber.
You don't seem to be considering a couple of things:
The "backed up by guns" (if you want to have a serious discussion, these sorts of libertarian cliches could perhaps be checked at the door) tax funded roads have benefits that extend beyond the road users. "Externalities" as it were, in terms of lower prices for goods that are easily and quickly shipped to the area, competition for other modes of transportation, and perhaps jobs in sectors like tourism.
If, ignoring the externalities, you wish to more directly attach the costs to the people utilizing the roads, you could raise gas taxes. Of course, that has its own positive and negative aspects, and winners and losers.
The real world is tremendously complicated, and I don't think it's really possible to predict everything. However, I don't think that means that you can simply ignore some of the more interesting facets of economics and say "errr, just let the market take care of it" - it's just too simplistic.
"When schoolchildren start paying union dues, that's when I'll start representing the interests of schoolchildren."
-- The late Albert Shanker, former president of the American Federation of Teachers, 1985
I'd prefer to let parents decide how best to educate their children. The entire system shouldn't be designed to accommodate the outlying parents you fear who don't care about their kids.
I think this is a step backwards. In the USA we have moved away from Who Should Rule? and Which Ideas Should Rule? and the focus is more on how should disputes be decided. Force is not a rational answer to that, and we have embodied this in our tolerance for queer and strange people/ideas, even disagreeable ones. The main feature of our system of Government is also about how disputes should be decided: it is responsive to changes in opinion of our citizens (via voting): when many people change their minds about an issue the government is changed correspondingly -- even about basic education. So disputes can be decided by persuasion instead of force.
It's worth noting that basic math or reading education are not presently required in some States, so requiring them would reduce freedom of choice relative to real life today. For example, in Kansas, there are essentially no requirements for home schoolers, including no record keeping, testing, or required subjects. http://www.hslda.org/laws/default.asp?State=KS
Math is a fundamental truth of the universe. I don't think any argument exists against the required teaching of these two subjects, other than stating libertarianism is always better.
If I was the dictator of the USA (or Equatorial Guinea), I wouldn't actually write the curriculum myself and force it on everyone. I'd get a board of experts and outsiders with qualified opinions to write it. Then the people would pass it by referendum, to give them that nice illusion of choice.
Two competing schools of thought about how to treat the best ideas we have today -- the ones we feel most certain of, and have the hardest time imagining a reasonable person could dispute -- we might call the School of Certainty and the School of Fallibility. The first believes our best ideas are the ultimate truth and wishes to set up societal institutions which best embody those truths. The second believes that it is important to remember we might be wrong and our vision is limited, so we should set up institutions with a focus on error correction, which means openness to new ideas and approaches, tolerance of differences, and not using force in the name of sanctioned ideas. The first school is more concerned with creating a good society by present day standards. The second is more concerned with creating a free society where people live by their own standards.
The School of Fallibility is often ridiculed. Certainly we aren't all wrong about common sense opinion X, it's so obvious. Why do we have to be so careful and cautious about even the most basic things? That's a lot of wasted effort, and it allows people to make huge, unnecessary mistakes and ruin their lives.
We live in a period of rapid change. Many mainstream, traditional, long held, obvious, common sense opinions have been thrown out in the last century. This story is well known for science, and civil rights and many other issues. But still people are complacent. We changed. We got better. What remains obvious today must be even more certain.
So, rms, perhaps I can surprise you away from complacent certainty by presenting an argument which you did not think existed.
I know a lot of people who don't like math, and who actively avoid using it in their lives. One can have a successful life today even in the extreme case of irrationally avoiding all math. Consider the adults today who dislike and avoid math: forcing childhood math lessons on them did not turn out to have helped. Now they have a grudge against the subject fueled by deeply unpleasant memories. It's harder for them to actually learn math now, should they find a use for it. Therefore it would be better not to require math lessons, and instead to let people learn it themselves on their own initiative if/when they find a reason to want to. We might call this approach Just In Time Learning.
I would be curious to hear your examples of someone leading a successful life while irrationally avoiding all math.
Perhaps you will reply they at least need to be able to count to 4 to hand back the right number of each coin. And need to be able to read numbers to answer questions like, "What does the Super Mushroom Burger cost?"
But the blatant usefulness of a skill is no argument in favor of required education of it -- won't people want to learn it voluntarily? And those who disagree, why can't you leave them alone?
Also, isn't is a bit ridiculous to call government schooling a success? It's failing in a wide variety of practical ways quite apart from any philosophical objection to the government deciding which ideas our kids are supposed to learn.