No...the topic of "simple machines" is pedagogically separated from the topic of "turning moments", the reason being that the teacher (who used to be me) does not want the student to get confused between the concept of work (force x distance moved in direction of force) and moment (force x distance from fulcrum). The fact that the two measures of distance are geometrically proportional in the lever tends to be an unnessary side issue for students at that level.
above, you linked a third degree lever with wheels as in wheel barrow, but if a wheel is presented as a constant lever, which it is, then you can easily tell why it has been so useful to humanity... Moment is certainly an element of it, but only an element... In fact, with other wheels, bearings to be exact, and lubrication, the moment reactions can be reduced to a point inconsiderable... In structural engineering, the force is met with resistencc... In the engineering of a wheel, the lateral forces, or the force of gravity, friction, or inertia might be more highly considerable than moment...In a building, moment forces must be resisted because buildings do not fall down, but twist down... Wheels are desgned to have little resistence to twisting on their axis...