Lot's of people, including several major open source communities and FOSS proponents. That was the goal of projects like KDE and GNOME, and smaller ones like Gnumeric, Evolution, GIMP, etc.

If not as a fully explicitly stated belief (which some did that too), the idea was nethertheless very prevalent that the endgames is: "we just replicate those programs and we take over the desktop with FOSS".