Also, why not integrate it with the search button? A button next to
voice search button or a long press on the search button (instead of
voice search)?
Yes I know that this could be done with a third party app but it
should be available in the stock app, it should be convenient to
access the gesture search, for example within an app or browser etc.
Its a hassle to access the program menu or home screen just to run an
search app!