Competiton for honors is only valid if the competitors all adhere to the rules....this isn't NASCAR if-you-aint-cheetin-you-aint-tryin. 

So, IF the administration's remark about competition being "very petty" indicates the school can't assure the winner won with integrity, then yes, shut it down. Otherwise, a long academic tradition of having a valedictorian should continue....no matter how boring the speech. :-)