Before rushing, a proof does not create equivalence; it reveals it under specific conditions, which must always be our threshold of understanding.
The equivalence between sensitivities based on fixed points and KKT sensitivities is conditional and not generated ex nihilo by the demonstration.
Our mandate is to consider the downsides and failure conditions, because the validity of this equivalence intrinsically depends on respecting these conditions.
If the underlying assumptions are violated, for example, during a major disruption of global supply chains for crude oil, the theoretical equivalence may become obsolete.
It is always necessary to identify what protects our positions if the model fails in a real market scenario.