Like kickstarter projects, they could even fund the research with pre-orders or even donations. Sergey and Larry have a brand name and could use it by simply endorsing research and the money would flow in.
They might have gotten the idea the secretiveness is a good strategy from Apple, but that confuses correlation with causation. Apple succeeded with solid build quality matched with solid software and some free marketing from early adopters fanboys.
So far, X Lab has failed to some extent. They've produced no solid products. Google cars, google glass, still nowhere to be seen. Opening up would allow a much larger number of people to contribute.
Large orgs haven't realized that in the age of limitless communication, the internet, the public can be more helpful than paid employees. Google should take the lead in encouraging the public to contribute and showing the rest of industry how it's done.