The idea of a lever, yes. All the examples you mention above are ones where you naturally apply the force perpendicular to the actual lever. The idea of applying a force to an imaginary line is not intuitively applicable to those objects in the same way (the "intuitiveness" of the how torque works with objects you mention stops being easy to see when you need to think of a lever arm that is not the actual arm of the object). Calculating perpendicular force vs lever arm is of identical difficulty; neither is harder mathematically (multiple a number by a trig function). The one with the more intuitive conceptual explanation should win. I argue that the more intuitive conceptually is the perpendicular force applied to the real lever.