I had this issue in a case I think is interesting; a customer had a database with incremental IDs of a certain product they sold. On a web platform, the product owner in turn could log in and view a list of their products and their status. The id of the product was part of the URL; /product/851. Of course, the product owners could not get any information on IDs they didn’t own, but the numbers gave away info on how many devices existed before them. And they wanted to hide that information.
Of course, there are many ways to solve that situation, but UUIDs is one.