Unfortunately for Spotify, court orders are ineffective against foreign nationals sharing information. Copyright enforcement is as futile as the encryption "export restrictions" the US and other countries tried in the 90s and early 2000s.
This isn't aimed at pirates as much as it's aimed at non-pirates, especially companies with significant assets.
They know full well pirates don't care, but it's a message to any company or entity seen as "too friendly" with pirates or that enables pirates to do their thing.
As much as I love Anna's Archive, I feel like this Spotify move was a misstep on their part. The music industry seems far scarier than the publishing industry when it comes to copyright suits, which means they have a lot to lose here by poking the bear, but there are already plenty of places to find pirated music, which means they also don't have much to gain.