Looking at your proposed solution again, a question popped up: if the UI can comfortably support an expanded search bar, then what's the point in minimising it, ever?
if there's enough space for an expanded search bar - there's no point, in my opinion.
But for example - on map based apps I would personally prefer to have the map with as little distractions (icons, buttons,text inputs, labels) as possible.
In Google's Android Chrome the url box is hidden once you start scrolling down.
I like that . And they probably have the data to show you that other people like that as well, because this 'hide-when-scrolling-down' feature is there at least a year or so, If I remember correctly.
