So proof of original authorship is a big issue in academia? You could easily create timestamped proof of having created a particular document, so is the issue more an insitutional one? Pardon me if I make sense, I'm a complete outsider to this.
Not all cases are clear-cut, especially where a plagiariser restructures the document, changes the wording, sources, etc..
So I don't think this is a problem that can be solved practically, or even theoretically. But there are certainly things that can be done to better counter plagiarism.
This idea would only work if everybody started securing some form of proof of authorship before sharing papers with anyone, which I don't quite see happening.