I’m a virtue ethicist so my reasoning will be a bit different to everyone else’s here but I’m sure the arguments can be adapted to fit other frameworks.
The proper standard for morality should be human well-being. It’s a reasonably simple idea. It doesn’t involve any abstract categorical imperatives but at the same time it can incorporate certain things being “goods-in-themselves” if they are a constitutive part of this overarching goal. Ancient greeks called this ultimate end “eudaimonia”, I’m calling it “well-being”, and it basically consists of all the lesser ends a person could reasonably strive for. In virtue ethical theory these lesser ends are the goods and virtues.
The NAP is simply a recognition of how diverse and individualised “the good life” is. Learning how to live a succesful life in co-operation with other humans is something that just can’t be legislated. Knowledge about what a particular person’s well-being consists of is dispersed and tacit and the future is uncertain so it’s impossible to plan what the best outcome is to every problem that may arise. What is required is for people to develop genuine virtue, especially the virtue of good judgement, then they can work out life’s difficulties as they arise.
Both of these are impossible without a commitment to freedom.
Broadly speaking there are two things necessary for a person to develop good judgement - that they are given the chance to make decisions themselves and that they are responsible for both the positive and negative consequences of their actions. No one should be making your decisions for you or guaranteeing you a bail out when you screw them up or you will never learn how to function intelligently. Therefore learning good judgement requires you having a right to make choices but no right to other’s co-operation.
Secondly, just like it’s impossible to develop good judgement without freedom it’s also impossible to develop any virtuous character traits if your behaviour isn’t self-directed. To genuinely demonstrate kindness, generosity, courage etc you have to have actually chosen to be kind, generous or courageous. There is nothing admirable about, say, giving to the less fortunate if you had no choice in the matter. There is also nothing contemptible about it (at least not in general). It’s just absurd to apply value-laden terms to behaviour directed by someone else. So genuine virtue too depends on having free choice in the matter.
I would argue that this makes the NAP the essential framework within which well-being can be pursued. As a political principle it protects the possibility of well-being and biases no person’s well-being at the expense of another’s. To violate the NAP is to make pursuing well-being to the same extent impossible and to privilege some members of society over others.
At the level of personal ethics the NAP is supported by many of what aristotelians call the “generic” virtues (traits that are admirable in everyone). Fundamentally it’s the choice to deal with others through persuasion (reason) rather than force (lack of reason), to respect other’s autonomy, to care about other’s well-being and to live productively rather than parasitically (and as this refers to a character trait I’m using productive to mean “productive relative to what a person could produce with their natural talents” so disabled people aren’t ruled out - you can be disabled and still have a productive mindset which is what really matters). The fact that life, liberty and property are good ethical principles can be seen my the fact that we only accept government violations of them. No one would tolerate private citizens ignoring them and if the government is the delegate of the people (which in theory it’s supposed to be) then it should be held to the same standards.
None of these reasons however should lead to an absolutist interpretation of the NAP, as though the initiation of force was the only relevant concern, which is why I would argue consequentialist considerations, are important even if they aren’t decisive, and in extreme cases can affect what counts as a proportional use of force to defend your rights. You couldn’t throw someone off your flagpole or kick them out of your lifeboat for example (though you could still claim damages from them). I couldn’t provide a fully worked out economic theory here but some of the same reasons that support a libertarian ethical theory support a libertarian economic one. The localised, tacit knowledge argument and the good judgement argument would both apply to resource allocation too. Probably the most common argument against libertarianism is that the poor would be systematically disempowered and left struggling to just get by. However I think the poor would benefit, disproportionately so, from a more libertarian system. There are three options the less fortunate have, starting their own business, working for someone else and charity. I think all of these would be made more attractive if the state ceased to externalise costs, set up barriers to entry and make factors of production artificially scarce (as a short, very generalised list). Whatever a libertarian system would do it certainly wouldn’t be involved in any of the above. Alas a full argument for this premise would take a while and this post is dragging on a bit.