The big problem with classical music is that the compositions are all in public domain, however most performances are not. Given the subtle differences between performances, algorithms are not smart enough to figure out the difference. In fact, even humans would have a hard time to distinguish between two performances of certain classical pieces.
Still sounds like a Youtube problem, not with copyright. The amount of false positives Youtube's copyright system has generated is crazy. It's clearly broken and wide-open for abuse by bad actors. Even with the complications of copyright there are so many examples of people having entirely fair-use videos taken down. It goes well beyond just the difficulties of two works one copyrighted/one not matching.
As an aside, without copyright, we could have both Disney and Sony Spiderman movies. The consumer wins, and there's more than enough money to go around for competing studios.