I guess that no one has tried it or, if someone has, they don't want to write about it.
I gave it a try. It is very time consuming, but the end result is quite good in terms of avoiding distortions when doing poses, better than anything I've seen so far with bone based rigs. And it has inverse kinematics, which makes posing a lot easier.
Most of the work is in fitting the skeleton control points and the "deformation cage" to the character. I think both of these things could be largely automated with MakeClothes, and I think that once you have built one BlenRig, adapting it to another character should be a lot easier, especially if they have similar proportions. That said, I've only gotten through the re-targeting process and am just at the point where I can pose the body.
For anyone not familiar with BlenRig, the difference from most rigs is that it uses a mesh deformation cage, which is a low poly mesh that fits over the character. It has bones, including bendy bones, but they control the deformation cage rather than the character mesh. The deformation cage then controls the character mesh. As I understand it, the mesh deformation cage has been extensively worked on to deform nicely, e.g. weight painting and shape keys, and the result is that the character mesh gets deformed nicely.
Edit: it also has a lot of "fix bones" that hover around joints and help make them deform properly, and lots of drivers set up. Plus the low poly deformation cage makes it easier to make shape keys and drive them.I positioned the hand, and inverse kinematics did the arm and shoulder positioning
I positioned the waist and IK did the hip and knee bending
Just checking that the loose form of the bent legs is at least in part due to the clothing
The squished lat issue is still there, but I think I saw something about it being addressed later in the process