A common component of a product category page is the sort menu. User could usually sort the products by price, ratings or from A-Z. I guess that you would use the alphabetical sorting to find a specific product that you already know the name of but to me this is a blunt solution. To me - a product autocomplete search box that could match letters both in the beginning and in the middle including product variations would be a more effective solution than to let the user wade through a lot of pages just to find the first letter that a product begins with.
Do you see any other benefits for sorting from A-Z that I've missed?