Honest question: Why would Obama be a good bet? Or is this comment a joke?
Obama as their chairman would be a huge win for Google, but I feel like he probably has better things to do. As a former president, being tied to Google would only hinder him in lobbying goverments for whatever he chooses to lobby for.
He would also be generally pragmatic, likable, and qualified.
[1] https://en.wikipedia.org/wiki/United_States_presidential_app...
If you polled him right now across worldwide audience about his stature, it would probably be north of 70%.