Oh I see. Long ago, Jens made the design decision to build Snap! on top of Morphic, which supports live coding better than the DOM does. So the text input box is implemented in Morphic, like everything else. The reason has to do with the handling of screen elements that overlap, but I forget the details.
So I don't think you're going to get exactly what you want here, but feel free to file detailed bug reports about specific things that don't work for you.