I found the following description in a book, “Search Patterns: Design for Discovery”, which I bought from O’Reilly Japan (Japanese Edition).
A solid taxonomy with clear categories and labels is enough. Perhaps a sitemap or index is useful to complement navigation, but search is unnecessary. In fact, adding search may be downright dangerous, since most queries will lead to nowhere.
On this site, I put a search box to search within the site, but I think the description above is right. In most cases, the search result contains nothing. I use a search box with appropriate words because I know the contents of this site. But visitors can’t put good words for search.
Most visitors come to some page of this site, and think what’s this site? then use the search box without the knowledge of this site. Not always enter at the top page of this site.
Considering this, I changed the settings of Google Custom Search to search from whole WEBs with a priority of this site.
It should be better than no search results.