This isn't so much analogies, more that the physics of natural systems means they're governed by 2nd order differential equations, so really do behave the same.
More importantly, they're all forms of energy and transferable. Power=IV=Fv=TO=PQ.
The analogizing comes from saying "I is like P and V is like Q", or vice versa.
2nd order ODEs are very common, and I agree that it is unifying to see different systems modeled by the same equation. But I think more fundamental than that is the understanding of "through" and "across" variables, the notion of a "port" [1], and series/parallel toplogies for combining two one-port components to form a new one-port component.
You could still make an analogy between domains, even if you don't have second-order ODEs. This is clear even from your comment because, note that a spring+damper is going to be a first-order ODE. You would need moving mass to store kinetic energy, in addition to the spring to store potential energy.