Ring flashes are often used in macro, so you can raise your aperture from 5,6 to 16 and such get a better dof.
BUT with the better dof of the ring flash also comes a flat and too even light. And with macro, shadows are important, to enhance details like scales or hairs, so the ring flash is both a curse and a deliberance.
There are people who have blinded parts of the flash to control the shadows.
They are ½ succesfull, but still the light comes from the camera and not from above or from the side, and that is impossible to do anything about.
I would say a ring flash is only meaningfull as a fill light as long as the main lights are quite a bit stronger.