We investigate thermal transport in nanowire composites with anisotropic fillers. Using Monte Carlo and finite element methods, we show that anisotropy strongly suppresses effective thermal conductivity, independent of anisotropy ratio definition, thermal boundary conductance, or filler orientation. Within a three-channel framework, the extended network governs heat conduction, but thermal transport is constrained by the intrinsic randomness of heat flux and by anisotropy-induced axial and radial conductivity bottlenecks. These results highlight the role of nanowire isotropy and the connectivity of the extended network in overall heat conduction, guiding the design of high-performance thermal interface materials.