It's not vital at all. The authority cones from having people who will lock you up if you disobey.
The fact that the language is "flowery" is an attempt to convey strict semantics using human language. The Latin tenor of legal language in Anglophone countries is a historical quirk. The wigs are because the legal profession is inherently backward-looking and there was a time when such wigs were normal. The theatricality of all this is incidental; a court's authority depends on none of it; it's the men with batons and guns.
The fact that the language is "flowery" is an attempt to convey strict semantics using human language. The Latin tenor of legal language in Anglophone countries is a historical quirk. The wigs are because the legal profession is inherently backward-looking and there was a time when such wigs were normal. The theatricality of all this is incidental; a court's authority depends on none of it; it's the men with batons and guns.