Paul Furman wrote in -
september.org:

OK, the noise is more the reason but posterizing can be a problem in
dark areas...

The only cameras I know of with even a hint of RAW posterization are the
Pentax K10D, which would profit from 13 bits instead of 12 at ISO 100 (not
for 200 or higher), the Sony A900 also with a need for 13 bits at base, and
the D3X when in 12-bit mode. These are only on the fringe of posterizing.

raising shadows in post for the deepest shadows, and in
skies where the color pallet is very limited. Doesn't the noise level
follow this same principle? Or is there an unrelated reason for the
noise levels paralleling tone counts?

Any posterization you see in a RAW conversion is most likely caused by the
math used in the converter, and nothing else. Of course, JPEG compression
does some posterization of its own, especially if you use too much NR and
it starts blocking up.