Generative design is almost always in SDF form. Things like point clouds, images, and 3DNN also dovetail nicely. SIMP in topology optimization is a good example also. I believe alot of SDF applications are still held back by mesh extraction. There is no silver bullet that can handle adaptive methods, sharp features, and generate a manifold.

SDF and mesh extraction are one of my favorite areas of research. I think it is very important for additive manufacturing in particular. The value will be hybrid SDF and spline methods for complex and highly integrated applications such as fluid and heat transfer or compliant mechanisms.

Modeling a box or cylinder with SDF isn't the right application IMO. Optimized topology for a given PDE is.

Especially with additive manufacturing, SDF's are far superior but still not widely used (but I predict this will change very soon). As others have said, many operations are much easier when working with SDF's, but specifically for AM, there are many operations like lightweighting that are extremely difficult to do "correctly" when using normal meshes. For simulations as well, an SDF makes things like voxelization, random walks, and basically everything else that is related to the topology of a part much easier.

Check out the company/product nTopology. It's IMO the future for engineering modelling and CAD for AM.

I used to work for an AM company and was essentially the internal evangelist that complained about STL's and "traditional" CAD formats that are proprietary or just outright a PITA to work with (I'm looking at you, STEP...)

Super niche, but SDF shaders are the approach used with the voxel art tool, MagicaVoxel, to help artists quickly generate geometry/shapes for their artwork.

I believe it is because sdf are very easy to do constructive solid geometry on. Intersect, union, subtract operations are basically free and robust. Where as with solid geometry robust csg booleans are highly problematic with rounding errors and edge cases galore.