Understanding how baryonic processes shape the intracluster medium (ICM) is of critical importance to the next generation of galaxy cluster surveys. However, most models of structure formation neglect potentially important physical processes, like anisotropic thermal conduction (ATC). In this letter, we explore the impact of ATC on the prevalence of cool-cores (CCs) using 12 pairs of magnetohydrodynamical galaxy cluster simulations, simulated using the IllustrisTNG model with and without ATC. Although the impact of ATC varies from cluster to cluster and with CC criterion, its inclusion produces a systematic shift to larger CC fractions at z = 0 for all CC criteria considered. Additionally, the inclusion of ATC yields a flatter CC fraction redshift evolution, easing the tension with the observed evolution. With ATC included, the energy required for the central black hole to achieve self-regulation is reduced and the gas fraction in the cluster core increases, resulting in larger CC fractions. ATC makes the ICM unstable to perturbations and the increased efficiency of AGN feedback suggests that its inclusion results in a greater level of mixing in the ICM. Therefore, ATC is potentially an important physical process in reproducing the thermal structure of the ICM.