My shed is 8'x8' (based on available OSB sizing) built with 2'x4's and utilizing a "shed" roof (single slope). It has electrical hook ups and is insulated to suit my local climate. Was very easy to erect and has weathered well for almost 25 years.
See? Not overkill. But the need for insulation and wiring does preclude the use of 2x4 stud walls.
As a side note - I have an uncle who tried to build a house using only metric back in the late 70s as a way of supporting Carter's push for the metric system. He gave up after 3 weeks.
hah, 6' by 8' roughly, then. 2x4's a reasonable bit of wood for a small project?