One thing not mentioned in other comments is that stroke order also helps with software that wants to do character recognition. If, for example, you are taking

One thing not mentioned in other comments is that stroke order also helps with software that wants to do character recognition. If, for example, you are taking handwritten notes on an ipad, and want software to convert the notes into text... well, knowing the order of strokes and having an agreed upon order helps considerably over just trying to match shapes. Digital dictionaries also usually have a "handwritten input" mode to look up a character, and that mode will also recognize characters much more accurately when input with correct stroke order.