I work for one of the big three, though just a technical staff, so I am no where close to knowing the full details of how licenses are signed, but enough to understand at the high level.
I see your points and I think they are very real. Streaming is one of the biggest sources of revenue today for the major players. Territories in music industry is what's squeezing business like Spotify. You can have a deal such that Warner has exclusive right in North America for all licenses, and can then sell to Spotify. Then perhaps another deal is reserved to a Sony-owned label in Eastern Europe. So if Sony doesn't want to sign the deal with Spotify, sure, Greek users may never get to play that song on Spotify.
I remember jumping from Apple Music and YouTube to Spotify because Spotify offers by paying monthly subscription, I have instant access to many music catalogs. Unlike Apple Music, I had to pay $0.99 or whatever per album/song. I am not sure if that has changed since, but it was the #1 reason I left Apple Music.
Since the Big Three has made so much more from streaming deals, they are going to choke Spotify's throat, but also have to deal with Spotify. After all, there is a solid and a strong growth of active users on the Spotify platform.
Big Three will flex muscles, but they won't just let the deal fail. Both sides need the revenue desperately. Netflix is in the same position but it has been producing its original contents so Netflix is less dependent on outsider producers. I think Spotify will do the same: create its own label and production companies, sign artists and make deals with the Big Three at various levels. Perhaps even buy a show ticketing company. Maybe begin to create a broadcast and video platform.
Warner Music Group's owner (Access Industries) is an investor of Spoifty (Access Technology Venture is owned by Access Industries which owns WMG). There's a humor whenever I look at music industry: we play the game of music chair, because your ex-worker might just show up to your conference call the next day representing another music company. Since artist X may have separate deals with separate labels (which in turns separate music recording companies), or because WMG needs Sony's help in India or whatever, in conclusion everyone has a stake in Spotify at the end of the day, even if you are not a direct investor of Spotify.
Unfortunately, every dollar collected is split up 50 times just because it takes many parties to publish a music and then collect the money. Everyone wants a piece, and everyone will have a piece. The pie might be small, but just enough to feed.