Anthony Levandowski went to Uber because he is interested in furthering self-driving car technology into practical applications and Uber offered to actually, really prioritize his project and make his dreams a reality. That's the only logical explanation of his actions; he thought Uber would be a better technology and business partner.
Setting aside the legal issues of whether what he did was right or not, I don't think Google would be the right custodian of this project anyway. For the greater good of the world, we need self-driving cars to become a reality.
And Google just isn't going to do it. They are invested in self-driving cars like they are invested in contact lenses, or drones, or robots, or go-playing AI, and half-dozen other things. Uber was/is a far more logical choice for a company that is going to be both motivated and pragmatic enough to bring this technology to market.
Google has been working on it for ages and we have yet to see a serious attempt at a non-academic implementation.