Do you need someone to repeat what's scarce? The digital anything can be written down in the blockchain notebook with your name/key and it's yours then. Same as when you would get a C from your teacher who would write it into one of those big notebooks with everyone's names. That combination of your name + class + grade is the asset uniquely assigned to you. Now when you asked your teacher to change that C to a B, to maintain your average, that wouldn't be possible as the teacher would have to write a new record and we would all know that you had a C actually. But all those grades are your only and thus scarce by definition.
I would suggest that your argument doesn't pay enough attention to the second word in "scarce asset" -- asset.
These unique tokens almost always point to digital files that are accessible to everyone and anyone, and that can be viewed, downloaded and reproduced by everyone and anyone.
To the extent that a person might consider these files are "assets" at all, the bigger issue is that ownership of a non-fungible token is still just ownership of a non-fungible token. It doesn't on its own convey any ownership of or economic interest in the "asset" it points to. If you want the token to convey ownership or economic rights, you're back to the traditional legal and financial worlds Web3 is supposed to be supplanting.
To the extent that a person might consider the NFT itself to be an "asset", the question is where the value is derived if the NFT is merely a pointer to a digital file that you don't have ownership of or an economic interest in.
But why would you want your grade history to be public so that anybody can read it? And adjusting grades is a valuable feature, given that some teachers do really make legitimate grading mistakes that should be corrected.
The public aspect of the content is orthogonal to the public aspect of the data. E.g. let's say the grade record is encrypted. Anyone party to the key is able to verify that the record is (un)tampered, but the wide world cannot read your grade.
And that is orthogonal to whether the content is mutable or not. It just means that mutation is deliberate and obvious.
