Personally I love when mappers map their own music, however you should note that composing music and creating beatmaps are 2 different skill sets. You can rank maps on osu! without knowing anything about music theory. Similarly, you can be an expert in music but lack mapping experience.
One example is xiediacee's
Time-Skip-Pass, however as you can see it's a new mapper map. In general, a map where the mapper was the composer won't look much different than any other map, since there are other more significant factors (such as song genre, BPM, mapping expertise, etc.) that influence the outcome of a map.