I agree. I didn't think it would, but Chummer gave a character the bonus and I became curious. It is technically listed right under the heading: cyberlimb, in CF, and functions like a worse than typical flesh limb. I can see cyber-singularity as also a bit flesh-hating and see how someone would want to rid themselves as of much flesh as possible on their way to be more chromed, and to them, it is better to have an unmotorized prosthetic than their flesh arm. This character didn't get a prosthetic because of an injury, but out of intent.
I have a character who I am trying to fit a lot of cyberlimb 'ware. I was trying to see if I could get 3 better quality cyberlimbs and a prosthetic and then replace the prosthetic later and still get the Full Cybersingularity bonus. If I can't, it's better to just not get a fourth cyberlimb yet.