I think where things fall down is on hiring junior candidates, or people re-entering the job market after years out of it (like my wife). "Minimum requirements" in those cases actually have a very deleterious impact because they filter out people with intrinsic motivation or talent but slightly different experience backgrounds. Either by the HR person themselves (who usually doesn't care much because it's a junior position, etc.) or the candidate (who gets put off by the min requirements label).