I don't get why people seem to ignore this. If facebook added internet search to their site they would instantly become the second biggest provider. I would be very surprised if they weren't already working on this.
People go to FB to communicate, they go to G to search. Brands are associated with products. That's why this G+ thing is a bad idea, it totally waters down G's brand in search. FB offers Bing on their site, but still nobody uses that.
I don't think this is true for most people. This has been discussed on HN a few times. While the techie crowd usually has distinct sites for different purposes, this isn't true for most people. Facebook is the only thing a large number of people get on the internet for. Portals work at engaging visitors, it's just a matter of monetizing the eyeballs. Facebook has the engagement locked down, now they just need to monetize the eyeballs.
FB may have Bing search integrated, but its not in any prominent location. I've been on facebook for years and have never seen it, not once. Perhaps its integrated with facebook's people search? The point is, if they put a plain-ol internet search box on each users homepage it will get plenty of use. With the plenthora of data they're generating, internet search can be trojan horsed by way of a history/activity search.
But for people who are already on facebook its natural to just use the search box that's 5 inches away. For better or worse, facebook is the new homepage of the internet for a lot of people. There are endless ways they can monetize this.