I am having the same exact issue as everyone here. I started on iOS 6 and was working like a champ. The moment I upgraded to iOS7
Deleted All Spotify Data - No effect
Deleted All Spotify Data, then Deleted App - No Effect
Deleted All Spotify Data, Deleted App, & Restored entire phone - No Effect
It doesn't matter how many times I restart, what I have running, or where I am logged in at.
The only thing I have noticed is that if you store music on your iOS device it makes the device do this. If you store your own music it makes it about 20 times worse. I only have this issue on my iOS device, and it is getting a bit ridicious nothing has been done about this yet. I deeply regret upgrading to iOS7 because it crippled my main function of my phone besides calling people and checking email.
I gave up. There are parts of Spotify I love but for now I've gone back to the free version and am paying for a different service for now. They don't have all the functionality that Spotify has, but they don't insist on the inaccessible black background on my Mac - and it just works. Wish they could combine the best of both.
Yeah, I have to admit that even if I use it everyday, Spotify turned pretty annoying. It's still sluggish on my iPhone, and i still have troubles syncing local files and offline availablity. Also, none of my albums are available offline, if I'm not connected to the internet, even if they're checked for offline availability...
… and Spotify was so great for a while there… You screwed up, guys!