Unlike piracy, when you pay for a service, you're making a judgement about the service as a whole. Many people are willing to use a couple different free services, but probably not piecemeal paid services to get the same experience. So, unlike piracy, Spotify has to have a catalog that makes most users think "yeah, they have all the music I want to listen to". Especially as a top artist, Taylor Swift has a lot of power in this relationship, because of the impetus that Spotify has to provide a "full" catalog.
Hopefully, this model continues, and artists like Taylor Swift continue to push back. The system of 20 years ago had too little power in the artists, too much power in the distribution, and too little choice for consumers. I like that the middleman / channel delivery is now the one who has to provide value, and the artists can take their music elsewhere. It gives artists power, allows competition in distribution, and provides more consumer choice. We could go too far along any of those axes, but this sort of fight is, imho, pushing things in the right direction.