Firefox and a Windows VM are the major reasons for me to reach for my mouse. There's also nm-applet, and obviously gimp and inkscape, but I rarely use those. Oh, and cut'n'paste tends to be easier with the mouse, though xsel can sometimes be useful. Everything else can be controlled from the keyboard. (Like the OP, I use XMonad as well.)

For videos in particular, mplayer can be controlled purely by keyboard. There are GUIs for mplayer (I seem to recall anyway), but I've never used them.

Whether this is the right setup for anyone in particular depends on which apps they use often. Not everything maps nicely to the "everything is text" doctrine. But where it does, the wins are major: text is super easy to handle, index, search, generate. It's easier to record macros to handle text than to do GUI stuff. It's easier to write little tools to process and generate text than to do anything GUIish. Output of these tools again is text, so it composes in the same way that shell pipeline does. Version control works best with text. It's like tarpit of win, the more you dig in the more sense it makes :)