Forgotten opportunity

You ever wonder why no one ever seems to focus on google search box offered at google adsense? It's been a mystery to me also. From what I hear from other webmasters no one wants to give up their traffic to google and other sites. And also the fact that many people already use google they see no point in using these small boxes from other people's sites. Of course we can't overlook the fact that it makes little or no profit when users do use the search box. But to me this is just another emerging opportunity from the folks over at adsense. Think about it, the search can be customized to search only your site so you don't need a search feature on your own site. Also look at this as a way to increase the amount of diversity in your google ads. It appears as if more people decide to take advantage of this feature more advertisers will jump on the train. As for now adsense search seems to only be useful to homepage websites. Since no one else wants to give it a chance.