"I guess the question is whether being Google CEO is the place to start your executive training. I can say with some assurance that if [Page] went to apply for the CEO job somewhere he wouldn't get it," said Allen Weiner, another Gartner analyst.

Valdes wondered if the behind-the-scenes scenario involves Schmidt stepping down voluntarily as a result of fatigue after an intense decade at the helm, and Page taking over on an interim basis until a new, more permanent leader is found.

Analyst and publisher Danny Sullivan at SearchEngineLand.com . "The two cofounders are notoriously difficult to pin down for any event, such as doing major press interviews or conference appearances. Part of Schmidt's role has been to be the 'dependable face' of Google for such things. But being that face can take a toll," he wrote.

But Google was also overdue for a management change, Sullivan wrote, noting that a decade "may as well be 100 years of Internet time."

Steve Arnold, an analyst who heads the firm ArnoldIT, faulted Schmidt for leaving Google too dependent on search advertising. "It has not diversified its revenue streams in a meaningful way," Arnold said. The financial success that Google has enjoyed has been largely due to ad sales, and was probably little influenced by Schmidt, he said.