But that's irrelevant for a single winding inductor, right? In that case, wouldn't induced currents in the belt increase losses?
In my experience with mains frequency transformers the belt is not a winding, in the sense that it is not a single turn coil. There is a insulation foil that does not allow the shorting of the "beginning" with the "end" (forgive me for the imperfect terminology).
If it was shorted, it will carry a very high short circuit current, with resultant primary winding failure (if no other protection is installed)
No current flows through it, and it only purpose is to reduce the external electric (and sometimes magnetic) filed.
With toroidal transformers I had very good results in terms of external electrical
and magnetic field reduction using a
steel belt, made with the same steel tape that was used for the toroid core.
It was possible to increase the magnetic shielding with a two or three turns belt winding, but the added thermal insulation resulted sometimes in excessive temperature increases.