There are two macros to allow search. Livesearch and Pagetree. They present results in different form of which Livesearch does a better job. In big organisations where confluence is used by thousands of people for various purposes it does never make sense to search the entire domain and top search bar can be used for it if needed.
I (and what it seems more people) want to be able to add a search tool bar (mini google) on to a page that would search that page and all child pages simple. Working with labels is out of the question as again with many publishers people won't know/be doing it. Who can do add a feature to Livesearch macro to allow restricting it to a rootpage same as in PageTree - does not look like a hard job to do (copy paste the code from pagetree)?