Perhaps, as much as a blank piece of paper is intuitive, so too can be a single, empty text box partnered with a single submit button.
But the search results page? Easy and intuitive, it never has been, and it is getting worse and worse as search companies keep adding more options, suggestions, clusters, facets and widgets to try and help you make sense of the endless pages of results. Even the Google with its once pristine layout recently felt compelled to add more clutter to the interface, an explicit acknowledgement that the results they serve up simply are not good enough.
So how could the search experience be improved?
One way is to make the results better by asking just a little more of the searcher up front. If you are able to ask the right questions, you can infer much. For example, if, instead of a single submit button, suppose there were three; "animal," "vegetable," and "mineral." By forcing the user to select, huge amounts of ambiguous results could be eliminated. Of course, this approach impacts the simple, intuitive search box and button combo myth, but if the experience and results are better, does it really matter?
Another approach is to build applications and interfaces that integrate rules to constrain search queries to a specific business purpose or process. To quote from a patent currently pending (um, mine):
"This invention relates generally to software-based search technology, and particularly to rules-based (rules being any standardized set of principles or methods for organizing and structuring information (e.g. The AP Style Manual; IDEF, a business process language; the Marquess of Queensberry rules for boxing) searching via a constrained or guided query structure."You can read the full patent here should you be interested.
Bottom line -- attributing the property of "intuitive" to a text box forces a free-for-all environment that must cast too far and too wide, and demands far too much processing on the backend in the attempt to guess at user intent. Constraining the queries, either by empowering the user or by integrating them into the user experience, can more easily deliver better, more relevant information.