"This is inherently what the board of directors does."
That would be what the board of directors is theoretically meant to do. In practice it's extremely far from the truth, with board meetings being very infrequent and focused primarily on share price and dividends.
This discussion is not really about Google though: Google does actually have a very relevant board of directors with most of them being founders or directly involved in starting large tech firms. Many other companies (Nokia? Microsoft?) are not so lucky.
Interestingly enough on Google's board only Paul S. Otellini (previous CEO of Intel) and L. John Doerr (early Intel engineer and VC) have an MBA. 
I agree with your point about theoretical vs the reality of a Boards function. I should have been more explicit, I am disagreeing that Board of Directors are overlooked in MBA education. At least in my experience, the Board was discussed often.