"Whether or not it's good public policy to expressly add such a loophole to the exclusivity granted to copyright holders is an ordinary political question, not a Constitutional-law question.
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While you are technically correct, the likelihood of Congress passing such a law is miniscule, at best. The Constitution intended that the work of artists and inventors be protected from unauthorized copying.
That's the bottom line. Yes, the Congress might have the authority to set the limits to that protection, and they have done so, many times. Most recently, it was to extend that protection far beyond the lifetime of the original artist, in the case of copyright.
I'm quite certain that there is no will in Congress to dilute copyright law to the degree being discussed. As I pointed out, if a third party can remove or edit some parts of a work, then redistribute it, that editing could also be to add something to the work. Perhaps a scene of a buck rutting with Bambi's Mom would be something that could be inserted. Since the film is animated, a good animation studio could do the job, copying the style of that Disney film. Then, they could edit the scene in and make new copies of the film.
Or, perhaps, someone could edit "The Passion of Christ," substituting English dialog into it. That dialog could pretty much say whatever the editor wished, even blasphemous dialog.
That's why we have copyright laws...to prevent such abuses against works of art and literature.
If you allow editing and redistribution of others' works, it can work both the way you want it to and in ways you would dislike.
That's why, in practical terms, such changes will not be made by Congress, nor signed by any President, even if it is technically possible.
If Congress doesn't revisit the law, it will be because the law cited earlier in the thread already protects another method of getting the same result (special DVD player hardware and software that reads the unaltered original DVD and automagically skips the "naughty parts" based on a database listing). If that option didn't exist, I don't think the studios would have a chance of warding off a law that explicitly permits the creation of roll-your-own edited copies.