If you want to keep innovating, the company need to stay nimble, with the owner(s) only interested in innovation. I don't know, maybe that's why the startup eco system works.
Another model that seems to work as well is the "duel roles". For example, Jeff Bezos lets the MBA optimize the hell out of Amazon, while he can play with Blue Origin in his spare time and focuses on more innovative technology ideas. Again, this is possible because Bezos probably has far more influence at Amazon than Page at Google.
So if Page can't convince "the board and the big shareholders" I believe it means he can't convince Brin, not some horde of faceless MBA's or institutional investors.
Your assumption about Bezos relative influence over Amazon seems unlikely, as Bezos Amazon holdings and the lack of a similar share structure means Bezos has far less voting power at Amazon than Page has at Google. Last I heard, Bezos held less than 20% of the voting power at Amazon.