The mathematics of SDFs are arguably easier to define then that of ray intersections, even for boxes and spheres. For arbitrary surfaces the intersection may not even have analytic solutions (true for >5 order polynomial surfaces), perhaps you'd need iterative solvers, so SDFs generalize and facilitate this intersection problem. You can even raymarch really exciting objects like fractals!
You can of course triangulate your surfaces into tiny triangles and use raytracing or rasterization. But then you're plagued by inevitable little edges unless you have at least as many pixels as triangles, at which point your performance gets really poor. So SDFs are really exciting for extremely accurate (photographic quality) reproduction of mathematically-defined objects.
You can of course triangulate your surfaces into tiny triangles and use raytracing or rasterization. But then you're plagued by inevitable little edges unless you have at least as many pixels as triangles, at which point your performance gets really poor. So SDFs are really exciting for extremely accurate (photographic quality) reproduction of mathematically-defined objects.