Another interesting usecase is generating seamlessly tiling noise [1]. Admittedly this is usually done in advance where slower performance is fine, but fully or mostly procedural games could really benefit from it. Combining this with prime number-sized layered textures [2] gets you a very organic looking texture with only an upfront rendering cost, making it plausible to generate high resolution unique textures for everything in a game on the fly.
[1] https://gamedev.stackexchange.com/a/23639 [2] https://news.ycombinator.com/item?id=2419347