I would say no in the case of geography. Qgis is a UI disaster as much as Arcgis. Where you are right, is that they sell people to install it for you, teach you, and very often, actually use the software for you (I have seen more than once).
I do most GIS viz through the browser (client-side scripting + PostGIS + ad hoc servers). Took a while to get up to speed, but it feels so good being able to scale projects quickly and not rely on Esri.
As for math, I generally keep it on the command-line.
