I do no think I agree. I do not know which plans FaceBook has but implementing Web Search is very far from searching your own web site, even if you decided to do it via crawling. Relevance, Spam Prevention etc are very important and very challenging. Even when it come to crawl proper handling of many millions of sites with robots.txt broken HTML potentially infinite amount of content are some of the challenges which you do not run into with your own site.

Regarding Alexa – even if you select to trust Alexa on this I’d look at Reach rather than page views and in this case difference is much larger. With Google most popular search service works well if you find what you need with just couple of page views, with FaceBook however you can get a lot of page views per session of people communicating to each other.