Formality is about preserving objectivity. You don't submit papers to a peer-reviewed journal watermarked with a purple dinosaur in a suit for the same reason you don't submit a complaint to a court watermarked with a purple dinosaur in a suit. Scientific publication (despite its many flaws) is about the content of the publication. Everything else - tone, style, grammatical nuance - is prescribed by a style guide because it is otherwise irrelevant.

There are certainly bad judges that hide behind "the authority vested in them by the court," but reductively asserting that formality is about maintaining authority misses the point (and the operating philosophy behind creating a fair and impartial court) by a country mile.