Interesting question! Let me address the points you make and ask about. Like the other answers, I will take the liberty of discussing not just your literal question but some of the other issues you raise, which I find quite thought-provoking.
I'll be honest:
That's a good idea, especially since you are posting your somewhat misguided beliefs in a public forum from a user profile that clearly reveals your identity.
I define plagiarism as misrepresenting who wrote (or provided the
ideas of) parts of your papers.
Okay, that's a reasonable way of putting it.
I don't believe you can self-plagiarize.
Hmm. I think you are falling into a common trap here that is related to the unfortunate and rather misleading terminology associated with the behavior referred to as "self-plagiarism." Indeed, when you submit your own work you are not "plagiarizing from yourself" in the sense of "misrepresenting who wrote parts of your paper," since you are claiming that the paper was written by you, and indeed it was. Rather, self-plagiarism involves a misrepresentation of when (or in what context) the work you are submitting was written. It is an unethical thing to do, but for slightly different reasons than plagiarism, and it is not a special case of plagiarism; it is quite a different offense.
If the goal of the assignment is to teach you something, and you
already learned it in the past (by writing a paper that fits), I see
no point in the busy work of making the current paper different enough
just for the sake of it.
But are you not assuming a rather narrow interpretation of "the goal of the assignment"? Would it not be equally plausible to say that "the goal of the assignment" is to increase your knowledge of a certain subject? In that interpretation, if you have already learned "something," the assignment would be an opportunity for you to learn even more about the "something" in question. Rather than submitting the same work a second time, you could reach the goal of increasing your knowledge by expanding on your earlier work (as Ben Voigt suggests in a comment), and achieve an even deeper level of knowledge and understanding, and do all of this without needing to work any harder than any of the other students.
Now, it's not for me to say that my interpretation of "the goal of the assignment" is correct and yours is incorrect. That's really for your university and professors, who are the ones giving you the assignment, to say. However, I will point out that my interpretation is motivated by a desire to maximize the new knowledge I gain from a given situation I find myself in, whereas your interpretation seems motivated by an apparent desire to minimize the amount of work you put in for your classes. A good university will definitely want to appeal to students like me more than it would want to appeal to students like you, so I suspect it will agree with my interpretation (and I know this for a fact in the case of my own university).
And finally, to your actual question:
Could a student use their copyright of their works to prevent (or at
least seriously restrict and complicate) faculty's checking of
self-plagiarism in the future? Couldn't the student just not grant the
right to copy their works?
The main problem with this idea is that as a student, the legal rights that you have in practice are very different than the legal rights that you have in theory. Remember, you want something from your university: a degree. Because of that, the university can force you to voluntarily give up all kinds of rights that you might theoretically have, just by making that a condition for getting grades and eventually your degree. For this reason, your idea will never work. As others have pointed out, as soon as you attempt to exercise this right to prevent your professors from copying your work, or any other right that your university reasonably perceives as interfering with its educational mission, the university will simply insist that you must waive that right if you want to remain a student in good standing. I am not a lawyer, but I don't see anything that would prevent your university from making such a requirement.