The big 3 record companies have negligible investments in Spotify:
https://finance.yahoo.com/quote/SPOT/holders/
Even if they did have a non negligible interest in Spotify, that is not the reason it is a non starter. It is a nonstarter because everyone wants to listen to music owned by the big 3 record companies.
Insufficient people are going to be interested in paying for a music streaming service without Michael Jackson, Sinatra, and a whole bunch of other big names and old songs that span decades. And people want to listen to music on demand, and repetitively. People are not going to be signing up for 1 month at a time like video streaming businesses, because people do not consume music the same way as video.