My suspicion is that a lot of people feel the same way you do about paying a monthly subscription, but that it's just that working to curate their own collection and keep it synced between devices is well, work. It's like the same way that the iTunes of the world "beat" the Napsters: convenience.
But you've touched on one of the reasons I'm trying to de-Spotify myself. I have a lot of music that I've gathered from various sources over the years, not all of them represented by streaming services' catalogs. This includes small-time local music and stuff that's come out of Internet communities like Newgrounds and OverClocked ReMix. I want my collection to be fully representative of the things I want to listen to regardless of where it came from.