Basically, at some point this conversation happened:
Label: We don't want to upload our music to YouTube because we're afraid of piracy.
YouTube: We promise that won't be a problem. We'll work with you to ensure you'll be happy with the state of things on YouTube.
The current system was born of that and nobody gives a hoot about the small/medium players who get screwed over by the insanity.
No surprise there. Encouraging small creators may have been necessary at some point, to increase user base, but at this point it's the creators that are compelled to be on YouTube, because that's where the audience is. Meanwhile, as long as the big labels upload their official music videos to YouTube, the userbase is pretty much guaranteed.
False negatives are a problem, because big content rights holders get upset. False positives rarely matter.
Not to ignore cases of manual copyright flagging abuse, but that's usually done for vindictive or careless reasons; there shouldn't be any reason for anyone to flag a video of someone performing an old classical piece.
Neither users nor even copyright holders really have that power (at least against automated system). Consequently, it seems like there's nobody in the room pushing for better outcomes for false positives.
And I, too, am angered that there's no option in the contact from YouTube for "this is a fraudulent or false claim. I own this material."
YouTube should tell BMI, Sony, DG, to be more careful when flagging amateur performances of classical works.