What causes the anti-siccative effect of soot (amorphous carbon) as a pigment in oil paints?
According to the Wikipedia page on oil-drying agents (emphasis added): 


  An oil drying agent, also known as siccative, is a coordination compound that accelerates (catalyzes) the hardening of drying oils, often as they are used in oil-based paints. This so-called "drying" (actually a chemical reaction that produces an organic plastic) occurs through free-radical chemical crosslinking of the oils. The catalysts promote this free-radical autoxidation of the oils with air.


The exposed surfaces of carbon black are highly functionalized, in many cases with oxygen-containing moieties.  The Birla Carbon website indicates that this surface chemistry "is a function of the manufacturing process and the heat history of a carbon black and generally refers to the oxygen-containing groups present on a carbon black’s surface." Per panel 3 of the figure at Asahi Carbon's page, "Carbon black properties," these functional groups can include at minimum carboxyl, hydroxyl, and carbonyl (aldehyde/ketone) functionality.  The section of the Wikipedia page on carbon black describing its surface chemistry indicates that quinonic, lactonic, and phenolic groups may also be present.

Most of the above-mentioned functional groups can participate in radical reactions, including reactions with the active species involved in paint hardening.  These side reactions of the carbon black siphon off the active radical species in the paint into pathways that do not contribute to the hardening/drying process.  The Lamp Black page on the Natural Pigments website provides support for this (emphasis added):


  However, [lamp black] is not generally recommended for use in oils, because carbon is an anti-oxidant that greatly slows the drying time of oil paint.