I think if you were at the mercy of the traditional record industry for licensing and you went an signed an artist to your label whose contract was up with say Warner Bros Records you could expect some pretty unfavorable terms in licensing content from Warner Brothers in the future. This is just one example but its a slippery slope.
It would certainly be much better for artists to get paid directly from the streaming provider, no doubt about that. But I think if you are out promoting that business model you are going to find it harder to license content from people business model if based on the "old way" of doing things. I think would have to forgo licensing from them almost entirely and carry only original content. This is more or less the model that is/was Tidal. I don't think has worked out too well for them.
In this regard there has been some criticisms against most of the current streaming providers as simply "propping up" the oligarchy of the big 4 record labels.
Record contracts are exclusive. Beyonce can't go and record an album for some other records label whereas in the Netflix model those actors aren't exclusive to Netflix. They are free to go out and make movies for Universal for 20th Century Fox when their series wraps for Netflix. As such it doesn't threaten the business model of the studios in the same way Spotify becoming a record label and paying artists directly from streams might.
The other difference I think is that consuming Netflix tends to be a concentrated experience in that you sit down to watch a movie or else you binge watch during a whole Saturday while the weather is crap. Music on the other hand is more passive. People play music pretty endlessly - while at work, on the train, at the gym. I think it would be much harder to be majority original content streaming service with music while keeping your existing subscribers satisfied.
So in the end, if everyone follows this trend, you'll have to subscribe to 3-4 different services at $10/month to get a complete library, and each will be trapped into different apps, so you could end up no being able to play songs together.
Unlike Netflix/Amazon/Hulu, where you could easily subscribe to or drop one month to month to watch different shows.
Netflix can produce a series which you will watch once and seldom see again. New content is king.
In music you mix old with new. If you lose the old content you will greatly limit the listening experience.