The revelation
You have had a moment to ponder the question about the toolbar buttons. Some of you may have even gone back to the application, and ran it using different backends, realizing that all the toolbars follow their respective backend's style. That would mean that it is somehow possible to include GUI-specific elements into our Matplotlib application. Or perhaps it is the Matplotlib figure that is the odd one out, with it being included into a tiny GUI application that is the backend?
Indeed, this whole time, you have been embedding Matplotlib figures into a GUI!
Everything in Matplotlib builds off the figure's canvas object. That canvas is the interface layer between the user and the backends. By staying above this layer, most of the messy details about GUI applications have been tucked away, keeping the user focused on their plotting tasks. Matplotlib's appeal is in giving the user a plot in as little as three lines of code: the import, the plot, and the show. Not...