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Spotify is unlikely to be licensed for this type of use. Only organizations directly representing the rightsholders can grant such a license. Having Spotify in the loop would only increase the cost to the end user, unless Spotify themselves arrange for such a license independently from Twitch (which would be interesting, but then there's no reason to ask Twitch for it).

There is a single industry association responsible for this mess - the RIAA. They're the ones using literal botnets to send thousands of strikes against content producers all over the internet. Since it's just one entity, I'm sure it's possible to reach a deal that's favorable to all parts. Compliance with the law for takedowns sent by smaller, less aggressive labels can be achieved in the normal manner.

You mean it's still a copyright violation. However, it keeps VODs and clips clean and safe from takedown requests, which is a huge improvement.

Multiple audio channels aren't that difficult to pull off, they're supported by MPEG-DASH and similar technologies (there's even a standard for it but I'm not sure to what degree it's currently implemented in web browsers). There should definitely have been multiple channels on Twitch a long time ago. Another use case is to allow viewers to manually adjust the volume mix between "Game" and "Streamer" (this comes up allll the time)