What is the benefit to using a paper filter in a moka pot?
Moka pots are essentially percolators meant for making espresso. As such, they are normally fitted with metal filters inside the pot that are capable of filtering some sediment, but not oils or Diterpenes (such as Cafestol). Diterpenes have been implicated in cholesterol increases associated with unfiltered coffee, but may also have cancer- and parkinson's-fighting properties. 

The paper filter will also have a large effect on the flavor of the coffee produced. Paper filters are designed to remove oils from coffee, but the oils removed by the paper filter can be a substantial source of flavor for the coffee produced, as many of the flavor compounds in coffee are fat-soluble.

Coffee produced with a paper filter will have less sediment, fewer oils and, in the opinion of many metal-filtered enthusiasts (myself included), a more even, less robust flavor. That shouldn't be regarded as an inherent downside, however, as many people prefer the flavor of paper-filtered coffee, finding the mellower profile and lack of sediment/oilyness preferable. Crema is more pronounced in metal-filtered than in paper-filtered coffee.