Are there ever cases where simpler shading techniques would be preferred, and if so what are examples of Flat/Gouraud being used over Phong? Distinguishing the differences between the three techniques in the bottom row with the most vertices is difficult, which makes me wonder if you are rendering a very complex object whether you would be able to "get away" with using a simpler and less expensive technique (or maybe none of this matters because of GPU parallelization).
You can certainly "get away" with these. A lot of these techniques are used during the PlaySataion 1 and original XBox era. Nowadays GPU are so powerful we just do everything in per-pixel fashion
Using a less expensive shading method on an complex object sort of defeats the purpose of using such an expensive object in the first place. In fact, doing per-face shading can be more expensive than per-pixel when the object is so complex that each pixel can contain multiple faces.
Indeed, per-face shading will contain another sample question of which pixel shall go into which face. As the number of vertices goes up, it approaches supersampling and thus looks better.