So we can conclude that neither building a successful social network nor building a successful search engine is easy :)

I wouldn't be so sure. Bing is an excellent counter example to that statement. And not just because (from my experience) it doesn't produce the same quality of results. It's also about user adoption. MS built a reasonable, if not clearly superior alternative to Google and spend enormous sums of money marketing it, making it the default option on the default browser installed on millions of new PC's each year, and is has single-digit market share.

Facebook doesn't have those inroads on the PC market to leverage. They'd have to build something so much better than Google that it would make Google look like Yahoo when Google first arrived on the scene. At which point Google could probably stop sandbagging their own search efforts that favor ads space over results and make up any lost ground pretty quickly.

I'm also not confident in Facebook's ability to create high quality new products anymore. The most recent big successes have come from acquisitions. I suppose they might be able to buy DDG, but they'd almost immediately lose all of its users. And unless the still wanted to build their own actual engine, they'd have to rely on the goodwill of MS to continue getting most results via Bing's engine.