Are there any situations where untempered chocolate is better than tempered?
Tempering is a process used to give solid chocolate a uniform appearance and texture, as well as to insure that those qualities are shelf-stable. Most commercially available chocolate is already tempered to some degree so that it has a pleasing appearance and texture for customers to enjoy right out of the box/bag.

Tempering is required when the final product will be made of solid chocolate or the chocolate is a component in an unadulterated state, especially in candies that will sit at room temperature. These would include molded and enrobed chocolates such as chocolate bars, bonbons, leafs, and nests.

Recipes that add chocolate to other ingredients such as dairy, flour, and sugar can be made with either tempered or untempered chocolate because the structure of the chocolate fat crystals is no longer the dominant source of structure and texture.  Examples of this include cookies, brownies, ganache, ice cream, and cakes. 

There is no normal application where untempered chocolate is required and tempered chocolate could not be used.  The only application I have been able to think of where untempered chocolate would be desired/required is something made for the express purpose of training and/or testing chocolatiers or chocolate tasting professionals.