Historically, how could a proof create an existing mathematical equivalence?
The precedent shows that a proof reveals or demonstrates a relationship, but does not make it exist.
This fundamental understanding is essential to avoid conceptual misunderstandings in modeling.
As with the laws of physics, gravity existed long before Isaac Newton proved it and modeled it mathematically; his proof did not "create" gravity.
To claim otherwise opens the door to fragile interpretations that could distort our value judgments.