Neither of these systems hinges on the existence of a copyright system, and even if they did, there are many many ways to implement a copyright system. Certainly, you can't say I would argue that the system as it exists today flies in the face of both approaches. To understand why, it's necessary to understand the history of copyright. Both copyright and patents
Both patents and copyright were justified in a single clause of the constitution for the following purpose (and this quote comes directly from Congress in 1988):
"Under the U. S. Constitution, the primary objective of copyright
law is not to reward the author, but rather to secure for the public
the benefits derived from the authors' labors. By giving authors an
incentive to create, the public benefits in two ways: when the original
expression is created and ... when the limited term ... expires and the
creation is added to the public domain."
"While one great object was, by holding out a reasonable reward to
inventors, and giving them an exclusive right to their inventions for
a limited period, to stimulate the efforts of genius; the main object
was `to promote the progress of science and useful arts;' and this
could be done best, by giving the public at large a right to make,
construct, use, and vend the thing invented, at as early a period as
possible, having a due regard to the rights of the inventor. If an
inventor should be permitted to hold back from the knowledge of the
public the secrets of his invention; if he should for a long period
of years retain the monopoly, and make, and sell his invention publicly,
and thus gather the whole profits of it, relying upon his superior skill
and knowledge of the structure; and then, and then only, when the danger
of competition should force him to secure the exclusive right, he should
be allowed to take out a patent, and thus exclude the public from any
farther use than what should be derived under it during his fourteen
years; it would materially retard the progress of science and the useful
arts, and give a premium to those, who should be least prompt to
communicate their discoveries."
What we have today is an extreme perversion of this system. The content industries have become the very monopolies we sought to prevent. Copyright was originally 14-28 years maximum, but the content industries have successfully petitioned Congress to extend that to the entire lifetime of the author PLUS 70 years. And why not? They profit tremendously by doing this. But it doesn't help authors (who are usually long-dead), it doesn't incentivize the creation of new work, and it completely fucks over the public.
That might be too fine a distinction, but in any case, there are two main varieties of arguments justifying copyright (though there are also some others, advanced less often):
1. Utilitarian arguments, that copyright improves well-being in some important way. These divide (as I see it) into a more strongly stated utilitarian-ethics approach, and a more weakly stated public-policy approach. The stronger approach argues on utilitarian grounds that it is ethically required to have a copyright system, because of the moral good it produces. The public-policy argument makes the more limited argument that a country adopting a copyright system will improve the country's society, so it ought to do so (but is not necessarily being unethical if it chooses not to).
2. Right-of-the-author type arguments that argue for a property or quasi-property interest in ideas, or some ancillary things around ideas. This is somewhat more prevalent in French thinking than Anglo-American thinking, as suggested by the French translation of the word "copyright", droit d'auteur. The quasi-copyright category of "moral rights" is related to this, and can support some middle-ground positions, such as a belief that copyright itself is not a right, but that being accurately identified as the author of a work is a right (i.e. some kind of anti-intellectual-theft position, where it's ethical to copy a book, but not ethical to copy a book and claim you wrote it).
There's an extra level of complexity when you look at contract law, corporate copyright, and transferability. For example, some of the droit d'auteur based approaches consider it an immutable, untransferable right of the original author specifically, who can enter into licensing arrangements for the work, but cannot transfer or sign away their fundamental moral rights.