[kragen]

Yes, that's an excellent point, but I think the lever law is more general than that. For example, it continues to apply when the lever in question is stationary, even though no value of the forces involved would violate conservation. In fact, it holds to higher precision in that situation because your measurements aren't confounded by vibration and accelerating masses.

Maybe you can derive it from some kind of generalization of Hooke’s Law to cover nonlinear stress–strain relationships, elastic hysteresis, anisotropy, viscoelastic behavior, and so on, but it's not obvious to me what that would be. Also, I feel like the concept of angular moments acting to produce angular acceleration is simpler and more general than all that stuff, but I'm not sure if conservation of energy and geometry alone are sufficient to derive it.