Centralized administration of public goods through the State tends to fail because of the lack of the incentives that politicians have, They must spend a lot of time trying to maximize their personal interest (power, Money, Influence, Votes) with the remaining barely to maximize social benefits which will fail that without taking in account that Democracy and voters also doesn't act rationally, They will prioritize bad biases and will chose bad policies and bad politicians (Rational irrationality, Concept that economist Bryan Caplan expands in his book The Myth of Rational Voter). Also, Philosophical arguments to support the State fail to do so as philosopher Michael Huemer demonstrates in his books The Problem of Political Authority.
Anarchocapitalism doesn't mean that there will not exist public administration it means that public administration, Political communities and other social organization should be voluntary instead on the base of arbitrary use of violence. Economist Bruno Frey has a interest model called Functional, Overlapping, Competing Jurisdictions.
Yes, all correct ethics, that follow the logic of consequence and accept that the individual owns itself, is predetermined to eventually find anarchism as the most moral system. Whether it's viable as an actual scenario is debatable. None the less, using coercion wouldn't be profitable for a company in an industrial society, that's why the northern states abondoned slavery in the US before the southern states: it was more profitable for industry. So to say that a state would spring up again naturally is unlikely. Further, anarchy doesn't mean the absence of rules in society, it just means that rules would be socially enforced rather than coercively, which is more efficient and moral according to me.
Humans are at their best when they are completely free to engage in mutually beneficial exchanges—when they are free from coercion (the use or direct threat of violent force against another person's property). Even the limited government in libertarianism requires the use of coercion. It is not possible to morally justify the existence of government to even the slightest degree, because all taxation is theft. And so libertarian philosophy must be taken to the conclusion of having no government at all.
Even animals down to the least of animal species have certain hierarchies that they abide by. Humans, as intensely social and complex creatures, are bound to follow the same rules and have even more complicated hierarchies because of our brains and nature of being social. There is no escaping government because it is in our very natures to have such things exist. This political philosophy fails because it fails to keep human nature in mind.
Anarcho-capitalism can't sustain itself for long in practical situations. The Old West of American history was one such example. Although it is a viable philosophy, money can't buy law and order in an anarchist territory. Eventually, the area will break down into complete chaos before adjoining territories will have to get involved and restore order.
No, I do not believe that private companies can control our police systems and other programs and expect it to work better than the system we have in place today. The democratic government that we have today is the best form that exists, and the system paying for our police works great.
Given the proponents of anarcho-capitalism I do not believe it is a viable political philosophy. I believe using this sole economic policy would more than likely lead to mass corruption and it would probably also lead to a massive over use of natural resources, further pushing harm to our own environment.