For what it's worth - it's a storytelling feature, too. In terms of the story, (and this is found in a number of cultures) something happens three times and the third time is when it changes. Or there are three characters (often brothers, or sisters) and the third is the one who breaks the spell/wins the prize/defeats the enemy. And in terms of the telling, adjectives and adverbs often go in groups of three (or sometimes two) synonyms. I've spent a lot of time in deep study of a 13th century Occitan story, and spent longer than I would like listing the occurrences of these repetitions.
One theory is that if you're dealing with oral performance (as would have been the case more often than not) it ensures the listeners hear the essential features or, in the case of the "rule of three", make sure they're listening for the third time to see what happens.