Perhaps a better way of putting it is that the CDTV/CD32 audio didn't have to go through the chipset it was just mixed into the audio output separately. That's why it could stream music whilst the games played sound FX.
Separating out the sound fx and music from existing games would be tricky simply because identifying where that data is on disk and/or in memory would itself be difficult.
Then of course the games themselves were written to be doing one, the other, or both and all of that would need to be rewritten for each game. Only we don't have the source code or original authors so it can be a big challenge to do.
This is all ignoring the cases where, as Bamiga2002 says the game actively manages the audio and switches things in or out, perhaps even changing the music tracks in response to things that are happening in game.
Newly written games might be able to do it however.
It's not a bad idea overall, but the implementation of it is probably not worth it for old titles.
