The widespread use of melt infiltration has to date restricted sulfur-carbon cathode architectures to only host materials processed as bulk powders with no site control of sulfur deposits. Here, we combine structurally designed hierarchical carbon nanotube (CNT) arrays with site-selective vapor phase sulfur infiltration to produce thick electrodes with controlled sulfur loading and high areal performance. Our results illustrate the critical role structural hierarchy plays in sustaining electrical connectivity to enable high utilization of the sulfur embedded in thick electrodes with high gravimetric loading. Here, a primary large-diameter CNT population provides robust conductive trunks that branch into a secondary small-diameter and high-surface-area CNT population capable of giving rapid electrical access to coated sulfur. Site-selective vapor phase sulfur infiltration, based on the capillary effect, controllably targets loading of one or both of the CNT populations to facilitate gravimetric loading from 60 wt% to 70 wt% sulfur. With the high areal loading of 6 mg cm-2, we demonstrate 1092 mA h gS-1 and 6.5 mA h cm-2 and excellent rate performance with >60% capacity retained at 10 times the discharge rate. Overall, our work leverages site control of sulfur incorporation into a host cathode enabled by controlled CNT growth techniques to emphasize the important principle of "quality over quantity" in designing high areal loading strategies with high areal performance and good sulfur utilization.