What's the purpose of the paper in NM-B cabling?
From what I can tell, the paper around the bare grounding conductor is simply a separator. Where as the paper wrapped around all the conductors, is there to hold the assembly together while the outer jacket is applied.


  
  Source
  
  with a bare copper ground wire wrapped in paper and laid 
  parallel between the insulated conductors. The entire assembly is wrapped with a paper separator before applying the PVC outer 
  jacket.
  
  
  Source
  
  4.) Separator: A suitable paper wrap, applied over the ground  
  
  5.) Assembly: 2 conductors and ground laid parallel and overall paper wrap or 3 and 4 conductors and ground twisted together.


It can have a negative effect, if the cable is exposed to liquid.  According to Underwriters Laboratories


  In general, cables with PVC insulation and jacket can withstand immersion in clean water for a short period of time without being damaged as long as the ends are not immersed....
  
  If the ends of the cable are immersed for any period of time, however, the internal paper wrapping around the bare equipment-grounding conductor will absorb and transfer the water into the cable assembly. The water may then start degrading the insulation or possibly corrode the conductors. If the cable comes into contact with contaminated water, the contaminants may also act on the insulation or conductors. Over time, failures can occur.