The realpolitik answer is that this is where the barbed wire ended up in the war between copyright holders and internet companies. It's a situation that satisfies nobody, but both sides get to continue making money. Justice has very little to do with it.

Performance copyright applies to classical music as much as for everything else. You're free to play, record and distribute copies of Beethoven's Symphony No. 5 as the copyright to the composition has expired, but you're not free to redistribute recordings of someone else performing Beethoven's Symphony No. 5 without the explicit permission from the author(s) of that performance.