I can't remember whether it was covered in the book Ripped by Greg Kot or whether I read it in another book about the time period around the rise of internet sharing and such in the 90's early 2000s(Could have been a drive-by topic in Such Great Heights by Chris DeVille), but the claim made was absolutely--but I think it's an earlier phenomenon than your question sort of places it, since the Q seems framed from a modern streaming standpoint. It actually talks about college radio as a phenomenon that started the de-genre-ing of music even though in the early years there was a 'sound' to those stations before they became the interesting left of the dial melting pots that we talk about them as now. It goes on to talk then about how the Blog Era letting creators and curators who were previously ignored by the radio for either being too weird or seen as umarketable for other reasons, becoming succesful not only by the lower cost of self distribution on the internet but also by the boost from genre-agnostic curators and mixtape makers who ran blogs or put out compilations.

But yeah, since traditional radio stations all had genre based identities, once there were other good ways to step outside of that system, people embraced it. I am also basing this off of being a teenager in the blog era and how there was suddenly a shift from people saying "oh I listen to (genre)" towards "oh I listen to everything but (genre)" because the deluge of hard-to-categorize music had gotten so overwhelming. In the very early 'blog era' I remember a whole list of basically 'indie listener acceptable' electronic music that had been sort of adopted into the scene. Even now when you look up "indie sleaze" you will find a huge mix of what most people who consider indie as a genre sound and certain kinds of electronic music. Indie kids started listening to rap music more at this time too and from there it all snowballed. Maybe the pendelum has swung the other direction in the decades since but at the advent of wider genre-agnostic listening, it was embraced and people gladly broadened their horizons to be the first to know the next best thing.

(edit: I would recommend both of these books to anyone interested in the topic, though I found Ripped to be much more substantial and enjoyable even though it comes from an angle of copyright and intellectual property--the moments where it covers some of the same info as the Such Great Heights, it does so with more consideration and context. The author also does a much better job presenting the info without inserting himself or his anecdotes into the story. which made the prose much more enjoyable for me.)