Not sure about them having zero incentive to make it thrive. They have invested a fair bit into the whole WCS structure, and LoL's success has to be enticing. I think they're slowly moving towards doing what they need to do to make SC2 a more popular game. This 2.1 update has taken some nice steps in that direction. I love the free arcade, BW music and extension mods. Expanded clan features also further that goal. Those are all really positive things for the game and community.
As for which games to play.. I love Nexus Wars personally. It's easy to get the hang of and you get a feel for some of the counters in SC2. Also easy enough to play successfully when drunk, lol.