Cover bands are bands playing other peoples' music. That's an expected use case in our legal system, and the authors of the music are compensated as mandated by the government.

Misrepresenting who performed an audio track is exactly that, a misrepresentation of goods sold. There are laws for that.

There is nothing in law that explicitly permits what AI sites are doing with performers' music. And the sites are not compensating the imitated performers. That's just plagiarism which is already unlawful.