It has been suggested but I'll tell you a few negatives and maybe other members could weigh in with their opinions.
1. You assume that the default search for members is searching for recipes on their own Bookshelf. But many casual visitors and new members will actually be searching for books in the Library. If someone who isn't yet a member clicks the magnifying glass they will be very confused because they do not yet have a Bookshelf. And a new member will be confused because the Bookshelf will be empty and they want to search for books to add to it.
2. The search box will just be the word search which loses out on many features of search provided on the Bookshelf Recipes page - filters (which give much more precise results), bookmarks, books/magazines/online/video/Preview filters.
3. Your Bookshelf Recipes search is only one click away anyway - hover over My Bookshelf tab at the top then click Recipes and you are where you will be by one click on the magnifying glass. So in terms of time and effort, what we have is not really different.