People espouse points of view that may not necessarily be what they truly believe, but are more radical than they are in order to gain attention. Its true that anarchism itself would not work, but a form of radical capitalism with much less government over sight would, overall, be better than current pseudo-socialism.
It would make a commodity out of everything. Private military forces could be assembled by the highest bidder, and there might not be a unbiased force capable of preventing them from doing whatever they wanted. Furthermore, without any regulations or control, people would abuse the idea of "private property." Land would be bought up by the rich, and the poor would be left even more homeless then they are now.
Any movement involving anarchy, especially capitalism, would doom a country much quicker than democracy. While capitalism might produce success in a democracy, not have the rules associated with the latter would produce a hectic amount of economic stress on a country. Democracy should always be part of government, especially to keep the tenants of anarchy at bay.
No, I do not think that a society following the principles of this government would be more successful that a democratic society. Throughout history it has been shown over and over that a democratic government is the best way to run a country, and is fair to all the people.
A democratic society is more peaceful with much less violence than one that subscribes to anarcho-capitalism. People won't kill each other for money and those who have money won't make the rules. The closest to anarcho-capitalism America ever got was the Old West where the railroads and gold miners made the rules and hired the gunslingers. That system didn't work very well, but it did what it had to until civilization moved further west.