There is currently substantial effort being invested into creating efficient thermoelectric nanowires based on topological insulator chalcogenide-type materials. A key premise of these efforts is the assumption that the generally good thermoelectric properties that these materials exhibit in bulk form will translate into similarly good or even better thermoelectric performance of the same materials in nanowire form. Here, we calculate thermoelectric performance of topological insulator nanowires based on Bi2Te3, Sb2Te3 and Bi2Se3 as a function of diameter and Fermi level. We show that the thermoelectric performance of topological insulator nanowires does not derive from the properties of the bulk material in a straightforward way. For all investigated systems the competition between surface states and bulk channel causes a significant modification of the thermoelectric transport coefficients if the diameter is reduced into the sub-10 um range. Key aspects are that the surface and bulk states are optimized at different Fermi levels or have different polarity as well as the high surface to volume ratio of the nanowires. This limits the maximum thermoelectric performance of topological insulator nanowires and thus their application in efficient thermoelectric devices.