TeV halos are regions of enhanced photon emissivity surrounding pulsars. While multiple sources have been discovered, a self-consistent explanation of their radial profile and spherically-symmetric morphology remains elusive due to the difficulty in confining high-energy electrons and positrons within $\sim$20~pc regions of the interstellar medium. One proposed solution utilizes anisotropic diffusion to confine the electron population within a ``tube" that is auspiciously oriented along the line of sight. In this work, we show that while such models may explain a unique source such as Geminga, the phase space of such solutions is very small and they are unable to simultaneously explain the size and approximate radial symmetry of the TeV halo population.