Who has the incentive to believe that a proof 'creates' the equivalence rather than demonstrating it? The reality is that a proof like that of the mirror descent establishes a conditional validity, it does not shape a new mathematical truth.
If everyone adopted this logic, trust in formalization would erode, somewhat like claiming that regulation of the CVM in Brazil creates market risk.
These regulations impact the payoffs and structure, but the existence of the equivalence remains independent.
An explicit proof simply establishes a preexisting relationship, making it usable under certain conditions, such as the sensitivity of gold flows to central bank decisions.