More importantly, they may sabotage their mission: If Spotify shuts them down, their exiting archives and especially future archives may be effectively lost.
(Edited for clarity)
Perhaps I misunderstood something, but according to my understanding
1. Spotify is registered in Luxembourg and has its operational headquarter in Sweden (Stockholm). Both are EU countries.
2. I guess it won't be Spotify that sues, but the individual music labels (very likely united).
But the real servers are hosted in kazachstan or russia I think. And they do not cooperate so much with EU courts.
So unless the EU installs a great firewall like china, they cannot really shut it down.
I occasionally wonder how many enormous collections of culture like that of Marion Stokes[1] have been lost because their curators made no effort to realize the value of their collection.
One may collect/archive now (when the data is, well, "available"), and publish later, when copyright expires and the material will likely be harder to obtain.