High-index dielectric (HID) antennas are a promising alternative to realize low-loss optical devices. Practical devices require simultaneous activity of many antennas working in unison, where the manner in which the resonators are arranged may influence their behavior heavily. Here, we study how the optical properties of bottom-up created amorphous arrays with stochastic distribution of HID elements stem from an interplay of the single-particle response and mutual coupling. We develop a theoretical framework that incorporates electric and magnetic dipolar interactions to prove that interparticle coupling even in random arrays is a key aspect. These interactions are responsible for a number of density-driven (i.e., minimum center-to-center distance) effects such as modification of directional scattering, significant enhancements enabling HID sensing, or efficient solar harvesting. Our results give clear predictions and guidelines how to utilize intra-array coupling to maximize the efficiency of such HID devices.