Copyright is simply the right to the fruits of one's own labors to be exclusive for some amount of time. I'd say that's a moral and ethical right. Just because you write novels or develop software rather than build houses or cars doesn't mean you should be deprived of making a living because others are free to duplicate your work with little to no expense, expertise, or time spent doing so.
Here is the difference: The constitution authorizes the legislature to grant limited-term monopolies to inventors and creators. But that isn't an obligation, and there is no underlying constitutional right. "Limited" could mean a week. It's completely up to the legislature.
In contrast, a law authorizing property seizure without compensation, or even an expiration date on property rights, would be unconstitutional. All copyright and patent protections expire.
They only expire because of an overwhelming public interest. Otherwise the very idea of them being property that can be created, bought, and sold would allow their owners the same rights as other property owners. They can expire your novel because it's useful (hopefully) to culture, but they can't expire your physical book except under exceptional circumstances.
I don't think that makes sense. They expire because they are disclosed, i.e. published, manufactured and sold, etc. Without a government granted and enforced monopoly, creators and inventors would have no protection against being immediately copied without compensation. There is no question of a "right" in this. It's a government granted monopoly, explicitly authorized in the constitution because, otherwise, such monopolies were considered abhorrent. In that, it is a unique part of the US constitution, and does not resemble in any way the rights protected by other parts of the constitution.
Those nonprofits you mention operate just fine without holding copyright in many cases.