Case in point, the article mentions Amazon. Amazon could easily hire the best and brightest mathematicians and developers to make the implementation completely rigorous and provably correct. However, they're still going to field questions from merchants saying "My product has a 5-star average, but this competitor's product only has a 4.5-star average. Why the hell is my product shown further down in the list?"
Similarly, you may work in the acquisitions department of BigCorp and you need to purchase some equipment. When you prepare your report for Big Boss of your recommendations, how do you explain that you are recommending something which has a 4.5-star average rating instead of the 5-star average rated one?
The ratings may be 100% mathematically sound, but the users of the rating system are not the same as the producers of the rating system. So it's largely irrelevant if the producers made it perfect if the users don't understand what "perfect" means.