Now considering these two things: the low percentage of searches per visit and the queries being used I lean to the idea removing the search functionality altogether to un-clutter the navigation bar (the search function takes up 25% of the navigation width).
My question: is this reasoning sane? Or am I overlooking something?
The Search feature doesn't need to be included on every website but if a few users need quick access to a document/page they have the option to search. The search feature comes in handy as websites grow and documents/pages don't fit into the navigation structure.
The size of the search field can also be reduced if it's visually distracting. PatternTap offers many pattern examples you can use as reference to re-styling the search field.
Ecomangination has a good example using limited space for their search field. Using a magnifyinemagnifying glass to represent search when a user clicks the icon it expands to show users the search input field.
Ecomangination Search Example