I never use the search box on websites. This site has one, because WordPress provides it by default and it would seem silly to remove a possibly useful feature. Most big name websites have one. Jacob Nielsen says “Search is the user’s lifeline for mastering complex websites.”
I’m coping OK without a lifeline and I have been for a few years. In fact, I am doing better than OK. I am wasting less time looking through dud results and instead, finding what I want through an external search engine, which today of course means Google.
This is not really a criticism of the people who make plug in site search engines, or even people who choose to make their own bespoke ones. Making an internal search engine that works when people search for a phrase that is in the document heading or for uncommon keywords in the document body is pretty easy. Making one that works well when people search for common words, use different vocabulary or misspell words is much harder. You could employ an army of semi-literate squirrels, to pour over a thesaurus and add meta data full of misspelled synonyms to every page, or you could just accept the fact that an army of semi-literate webmasters have already linked to your important pages using their own descriptions and allow Google to harvest that meta data.
Adding a search box is easy. Giving good results with variable input is hard.