Those who like to point to the constitutional origin of these forms of property should note where patents and copyrights appear in the constitution. They are listed as a power of Congress along with other powers, like the power to tax. They do not appear in the Bill of Rights where rights of individuals are explicitly described.
The constitution authorizes Congress to create monopolies for limited periods of time "to promote the Progress of Science and useful Arts." In this sense, patents and copyrights are explicitly linked to a public purpose. If it were determined that patents and copyrights are not the most efficient means for promoting innovation and creative work, and therefore Congress decided to stop authorizing these monopolies, individuals would have no more constitutional basis for complaint than if Congress decided that it didn't need to raise taxes.
Once we recognize that patents and copyrights are policies to promote innovation and creative work then the question is whether they are best policy and if so, are they best structured now for this purpose. Neither assumption is obvious and I would argue that the latter is almost certainly not true.
I think the analogy with taxes is both instructive and really informs the debate. Nobody questions that the United States government has the ability to collect taxes. But the level of taxes are set at the threshold that maximizes the general welfare and not as high as possible. In the same sense, intellectual property law should be set at a level that encourages/rewards creativity and not at the highest level possible.
In both cases the extremes of the policy are as bad as an absence of any policy. If you set taxes to ~100% then you'd end up with no economy (or a purely shadow economy). That would be bad. If you set intellectual property rights to too high of a standard then you have endless rent-seeking on the basis of a vague idea that was never properly developed.
This is not to say that property rights are unimportant. But it does illustrate that the way we define and reward these rights is a socially determined decision. The consequences of such decisions reflect the society in which the decision is made and not some sort of natural evidence of merit.