One prominent use case is: you can generate linear algebra kernels that are specific to both the shape of your data and the hardware features of the machine on

One prominent use case is: you can generate linear algebra kernels that are specific to both the shape of your data and the hardware features of the machine on which the kernel is run (i.e. on a Xeon use AVX512, on desktop use AVX2, or on really old desktop use SSE). Therefore you can avoid hand-coding dozens of specializations of such kernels beforehand.