Look up Roman armor. It's kind of skimpy. It would make no sense to have all armor meant to cover you up entirely, as the OP suggests.
Roman armor isn't skimpy, it covers the entire torso and the head (not the face). They wore leather skirts that went down to their knees and iron leggings. They also carried a hard wood tower shield. It was very flexible and lite compared to medieval armor, but it still protected very well and covered the whole body. You can have mobility without leaving your body exposed.