My two cents.
I would basically agree with your statements: to the best of my understanding, too, the rod has no other function, except mechanical.
However…
I guess we can have more insight by considering the reason why a thick metal rod is broken that way and in that very position.
Fatigue, no doubts.
So, if you look carefully, the profile of the rod is designed to act a kind of leaf spring, as it shall allow some play when the nuts are fastened, because you don’t want it to bite too aggressively into the ferrite elements, which are fragile.
So, we have a spring that brakes by fatigue at a corner (it’s where the mechanical stress accumulates).
Fatigue from what?
Here is where I step out of my comfort zone, but I guess the pulsating frequency of the alternate current is inducing some feeble but periodic mechanical stress on the assembly, eventually leading to the failure.
Pushing my speculations one step further, once the assembly is no longer tightly kept in place, the same vibrations that have caused the failure of the rod may cause some interruptions or alterations of the magnetic circuit at the mating interface of the two U-shaped ferrite elements, resulting in an unstable output of the circuit.
