History rhymes here, and the idea that a proof 'creates' an equivalence of sensitivity is a simplification that ignores antecedents.
The past teaches us that these equivalences reveal existing relationships, do not invent them, and their robustness has always been conditional on the underlying assumptions.
When market conditions diverge significantly, as during the European sovereign debt crisis, models considered equivalent have shown crucial failures.
A proof simply validates a mathematical relationship; it does not confer an intrinsic economic reality or unlimited stability to that equivalence.
The historical record warns that without caution regarding the conditions of application, we risk overestimating the reliability of these demonstrations.