@ekklesiagora - First off, I would recommend not classifying the position of any group based on specific philosophers. They helped generate the position, but they did not necessarily refine it, nor do they define it. That's bordering on a strawman argument, designed to discredit the entire philosophy by shooting the messenger.

Secondly, there is a difference between a morality standard and an ethical one. One is purely internal and subjective, the other is purely external and objective. The NAP is an ethical principle (do not use aggression), not a moral one, and as such it deals with actions, not inaction.

And before you say "inaction is a type of action" that is a non sequitur. They are both choices one can make, but they are not both acts. Implying that inaction is an action creates a lot of logical inconsistencies in the foundation of any point built of that premise.

Now, onto the idea that the NAP is "morally bankrupt".

You make the claim that:

It is certainly more cruel to allow a child to die slowly from exposure or starvation than it is to kill them quickly with a bullet or a blade.

In both cases, as you described it, the child will die. In both cases the child will suffer, but one may occur over a longer period, while the other is painful but quick. In one case, inaction is the cause, in the other direct action is the cause. Direct action to end life is more reprehensible than inaction that could result in the end of life, because one guarantees death, and the other assumes eventual death.

However, the reality of that use case is far more complex. Abandonment does not necessarily imply death as inevitable in the real world. It is a high probability, but not 100%, unlike outright murder. The child could be found, given to an orphanage, given to a friend who is childless and barren, etc. This false dichotomy is not a logical argument, and it has been consistently debunked because of its inherent flawed premise.

I know Rothbard's arguments on women and children, and to be frank I also find them logically flawed. That said, I do not consider Rothbard an authority on anarchocapitalism or logical thought.

Now lets take the ancom lifeboat example you used of the capitalist starving his fellow man.

The second man is faced with inevitable death if he does not take some of the resources away from the first man.

This is a false dichotomy for at least two reasons.

1. The first man could build a fishing rod with the materials, fish for his food, and then either rent out his rod to the second man, or trade the fish for other foods from the second man. This is a voluntary exchange, and requires no aggressive action at all.
2. The second man could negotiate with the first man to gain that resource by labour. Why would the owner of all the food waste his valuable time picking food, when he can pay someone to do it for him voluntarily? The first man gets fed, and the second man can look to do other things with his recently acquired free time.

But lets assume for now that both points are, for whatever reason, not possible for the second man to do, and his only options are what you describe.

If the first man wishes to enforce his unjust monopoly, then he must initiate aggression against the second man and use physical force to prevent him from taking the food and water he needs to survive. AnCap property is actually predicated on the violation of the non-aggression principle by the proprietor or his representative. Capitalism is a system of violence.

Now, lets break this down. First, I'll ignore the fact that your argument seems to be claiming the negative right of property ownership doesn't exist.

Secondly, you have conveniently glossed over the fact the initial act of aggression is taken by the first man for stealing property from its owner. That is an act of aggression. The fact you don't like that fact doesn't make it any less an act of aggression, and the act of taking any property from another, without consent, is theft. Ergo, responding to that act of aggression with force is a defensive act, not an aggressive one.

This is a typical semantic distortion used by many ancoms to strawman the anarchocapitalist positions on liberties & fairness. By recrafting the narrative to put the first man as some eternal victim to the second man, they are able to ignore the actual actions and consequences because of the need for survival, and create false dichotomies that misrepresent reality in the extreme.

Now that the argument you have made via the Crusoe econ illustration has been correctly framed, and not presented in the biased way you provided, you can see (I hope) that the argument you are making is illogical.

It is equally illogical to presume that capitalism is "wage slavery". That is taxation (an entity forcing you without consent to hand over your labour). No one is forcing anyone to take a specific job in capitalism (which is more than can be said for where people have attempted communism). Capitalism only requires that people work, and that work is judged economically by merit.

TLDR? : You are not required to set yourself on fire to keep others warm.