I'm agnostic on whether Page is really responsible in any way for Google's decline. I joined after he stepped in. I don't know anything about Page, but he seems to be a bad judge of character because of some of the things he has allowed and some policies he's supported.
What happened post-Schmidt wasn't directly Page's fault, so much as a lot of the other executives were waiting in the wings with shitty ideas that they now saw a chance to push through. Execs will attempt that any time there's a guard change, and I can't say that Page did a worse job of handling it than I would have done.
I asked a successful business owner what the hardest thing was about being CEO and he said (paraphrased) that "The job is easy, in that you have the power to have work done, but the hard part is that everyone is fucking lying to you." I don't think Page is a good judge of when people are lying to him.
I don't think any of Google's triumvirate (Page, Brin, Schmidt) are bad men. I think they're very good men who built an admirable company and kept it intact for a long time. I think they lack something in the ability to judge character (mea culpa: so do I; I tend to be too trusting of individuals despite my intellectual cynicism) which is why a lot of the middle managers and executives are problematic.
Then again, 90% of the cultural rot occurred before Page. Google's hideous "calibration score" system wasn't built in a day.
Fire Larry Page. [i.e., it ain't gonna happen]