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Honestly, all my clients mention or have the search icon in their navigation. They insist on having a search icon. Some website is a obvious No (like a landing page) and some Yes because of the wide spread of data.
The medium sized websites are where I contemplate the most. Yes, it's nice to have a search JUST IN CASE. But by having too much icons or tabs, the website will increase the users memory load (I have a principle or rule to that I follow to always reduce user memory load). I believe a well designed hierarchy can dismiss the use of search icons.
Or do you disagree. Even WITH a good hierarchy (like well structured content), you should still have search.
Do we have any user research or case studies about this?