I believe some of those performances are old enough to have made it into the public domain, and some of those old masters are pretty good.
It's not 2067 yet.
It would have had to have been produced in 1922 or earlier.
Works published between 1923 and 1978 are protected for 95 years from date of publication. After 1978 it's 'Life of the longest surviving Author plus 70 years', which works out to 2049 at the earliest. Now consider for classical music that every musician in the symphony can be considered an 'author'. That can be hundreds of people, including a person in their teens. Hell, put a preschooler on the triangle or something. Still, consider that some are probably in their twenties and will survive into their 90s. That's 140 years.
Anyways, consulting the timeline of audio formats..., it looks like the 'best' recordings you'd have would be wire recordings, and the phonograph records/tubes could hold only about 4 minutes of sound.
So in order to exploit this you'd need to find an intact record produced before 1923(until next year), scan it and convert it to digital, as well as putting up with the fact that in many cases you'd be lucky to find a single song given the limitations.
It would almost be easier to pay a symphony to produce songs to be put into the public domain 'for the good of mankind'.