The transmission doesn't skip for 'any' reason. You'd want to replace the Diff itself with steel as well. The belt is not even in this equation, Your belt problem was a different 'issue'. The only way your belt could suffer from a steel idler gear is you had the belt far too tight and that was a mistake in the first place.

Thus, instead of the idler going as usual, saving the tightly wound Belt.
Your Idler didn't give and the belt could not 'skip' and belt boom.