Copyright does not and should not fall under the Takings Clause. The plan would muddle, not clarify law.

Harvard Law Review, “Copyright Reform and the Takings Clause,” 01-xx-2015, vol. 128, no. 93, https://harvardlawreview.org/print/vol-128/copyright-reform-and-the-takings-clause/#footnotes-container

The conclusion that copyrights are property does not mean they must enjoy the same strong Takings Clause protection as real property. For several reasons, copyrights should be entitled only to weaker, probably much weaker, protection than real property is. Indeed, copyrights are such a distinctive form of property that they ought to be considered “unique” for takings purposes.88

First, copyrights are usually classified as personal property.89 Personal property does not receive the same Takings Clause protection as real property — for example, it does not benefit from the Lucas per se rule.90 As the Court has explained, owners assume the well-known risk that the government, exercising its power to regulate commercial dealings (or its traditional power to declare contraband91), will render the property useless.92 The same thing could happen to a copyright. For example, Congress might render a microwave cookbook worthless by banning the sale of microwaves, or state obscenity laws might (theoretically, at least) render a copyright in an obscene work valueless.