Music rights are split into two traditionally, the songwriting copyright and the mechanical reproduction right. Previous to the internet, media sales mostly went to the labels who held hte mechanical rights and songwriting copyright was earned directly to the artist. So if you bought a CD the label gets paid, if you play a song on the radio an artist gets paid.

The music industry lawyers were incredibly smart when they passed the DMCA back before online music was much at all, and got internet streaming defined as mechanical reproduction so they got dealt in on streaming.

ASCAP, BMI, and SESAC, et al, which give large blanket licenses to cover most copyrights for songs charged well known quantity for licenses, and early music streaming services paid those. Harry Fox (at least at the time) was the clearing house for mechanical rights and there was actually no set rate or anything. DMCA created a compulsory license that Harry FOx would have to give, but the rates were not known at the time, so everyone was getting VC funding without knowing what anything would cost.

That rate is probably much higher than the songwriting royalties, so the music industry has succeeding in getting ahold of most of the money in a new format that was poised to benefit the artists directly.

I guess we should just be glad it didn't happen like video streaming and there are actually rights clearing houses so companies like Spotify and others can make compelling streaming services with very large catalogs, unlike the city-state video steaming where you need 3-4 services combined to get access to most of the mainstream stuff.