I think Page had the right idea, because if you look nowadays at people under 30 for them the Internet is represented by social networks, be it Facebook, Instagram, WhatsApp or even Snapchat, the internet/web represented by the browser and by visiting different websites via Google is no longer that important. I think Page realized that if Google doesn't hop on the social train they'll end up looking from the outside at a flowering walled garden in which they will have almost no relevance.
I think they had a similar idea after Apple's iPhone started gaining traction, it's only that in the case of Android Google's execution was an order of magnitude better compared to what they did with Google+. I wouldn't put the blame for the failure of Google+ on Page only, I'd also assign it to Gundotra, after all he was the man directly in charge of it all, Page's fault is that he chose and supported the wrong man for the job.
I think they had a similar idea after Apple's iPhone started gaining traction, it's only that in the case of Android Google's execution was an order of magnitude better compared to what they did with Google+. I wouldn't put the blame for the failure of Google+ on Page only, I'd also assign it to Gundotra, after all he was the man directly in charge of it all, Page's fault is that he chose and supported the wrong man for the job.