I think you assume the best of people while I assume that the Purge would likely happen based your philosophy.
The western world is so far from an egalitarian structured society simply removing hierarchy will never last.. someone would see it as a power vacuum and attempt to fill it to some degree. For example back to your post's topic that in an anarchist society you would condemn acts of aggression thus discouraging it. So what would stop a militia from forming to seek revenge against their enemies? Thus you have a self-governing group that easily go right back to the hierarchical structure by simply choosing a leader ... you will inevitably repeat the past over and over again.

The anarchist's philosophy seems to me to be extremely idealistic making absolute claims against rule of law and ignoring history/ human nature.

I am no fan of zealous traffic laws, traffic cams and parking restrictions are one of my most despised government practice. Yet they are a major reason why roads function and I think a universal symbol of order in society.

Go to Mexico City where they don't enforce simple things like red lights. Traffic is impossibly deadlocked because the human inclination towards greed takes over. It's an overcrowded area and no one stops at intersections, they keep driving through like a fucking congo line creating even more congestion. You might say that it is symbolic of the government's complete lack of authority which is why some areas of Mexico are controlled by cartels and a defacto military state forms just to keep a grasp on tourists cities.

Next Go to Austrailia where an overbearing government will take your license immediately for speeding. . . and as a result, rarely do people speed even a few KMPH over the limit.

It wouldn't be impossible for roads to be built the free market, just don't expect roads in rural areas to be built or maintained, I would predict it would be like the current way the telecom industry builds internet infrastructure. Areas without a profitable population of customers still use dial-up quality connections in the US because the infrastructure is privatized and not "Common Carrier" like electricity or telephone cables. Many times the Free Market is a solution however sometimes its really not in public sectors. I think most people would agree that US Federal-Aid Highway Act of 1956 sped up growth in the private sector. Now, it's a huge crumbling concrete mess and needs to be replaced by a new technology, a whole different rabbit hole...

Ireland has Gov infrastructure for internet and it is better and cheaper than the US. There are many reasons for this, building infrastructure is expensive and companies can't risk their high-profit-margin expending investment in fiber-optic networks because they are too worried about expending funds on marketing to compete with each other. (soon internet may be completely wireless in urban areas but thats a whole different topic)
I am all for scaling back government, however, the world is an extremely complex chaotic system that will not be restructured without conflict. I for one am not ready for the inevitable vigilante justice that would result from a true anarchist society. Unless you are advocating for a Minarchy, sometimes gov is necessary sometimes its not.