I think they are more useful for outdoor work where you have a moving model and you want her well lit as she moves. So you have one of the portable ring lights that you can walk around with (within limits). The shadows then become less of a problem because usually they are not even seen. But the ring light doesn't have to be the classic type that surrounds the lens, but can just be a back of lights that you shoot through such as shown in this photo:
The above setup cost about $100 to build (4 standard 40" shop lite housings that each hold 2 40 watt bulbs - and then buy daylight balanced bulbs as shown). The Lindsey shot in my previous post in this thread was shot with a portable version of a light just like this. The tip off will be the catch light in the eyes.
Here is another example (this one overly soft and has a color cast, but it was one I could find right off hand shot with the above pictured unit):
Because of its size, you generally get no background shadows.
Cheers,
rfs