The thing is, it’s only possible to “completely prove something to be true” in math contingent on your accurate interpretation of the steps of the proof and of its outcome.

The proof as a platonic ideal is infallible, but in reality, it gets fed into a fallible meat computer, and in practice, even very smart and careful people do make mistakes, often at the individual level, but sometimes as an entire community.

Two famous examples were apparent proofs of the four color theorem in the late 19th century, each of which were widely accepted for over a decade before being shown incorrect.

We have better tools nowadays, obviously, but these still only increase confidence, which is exactly what running simulations does.