They kinda did that with ChromeOS + Google Docs with offline mode. The problem for Google is that while it was a solid investment for MS to persue cloud services to compete with Google, I don't think it would have been a good investment the other way around. Chrome is really the only desktop product that makes sense for Google because it pushes people into their ecosystem online. Creating something like a standalone OS or a standalone office software would have gone in the "wrong direction" for Google, taking people off their site rather than taking people there.
Also on a total sidenote, if you told me 5 years ago that Bing would be a serious threat to Google I would have a laughed.
Also on a total sidenote, if you told me 5 years ago that Bing would be a serious threat to Google I would have a laughed.