IF his forte is operations, more Ballmer and Cook to a visionary, it makes sense. Put a new visionary in charge of Google, and start focusing on turning the other bets into self sustaining companies. Maybe split google up a bit too, make CGP its own bet. You could even make the case for Youtube, Nest/Pixel, Doubleclick, maybe Android. Refocus google on being an information sorting and calling tool, whether that be search, shopping, maps, gmail, photos.
Google could benefit a bit from the Bezos API memo AND a bit from the Jobsesque "singular vision not kitchen sink of requested features" refinement. Paring google down and giving sects more singular visions, while encouraging cohesiveness might need a Bain Capital type chopman, but after that is said and done, Alphabet Chief should be more important than Google Chief.
Pichai's job should be demarcing responsibility and org chart, giving focus.