In this theoretical study, we investigate both electronic and optical properties of core–shell InGaN nanorods (NRs) for light emitting diodes (LEDs). These structures feature active layers wrapped around high aspect ratio NR cores, thus allowing for an enormous increase in active area. Hence, efficiency may be increased by operating at lower carrier densities, mitigating efficiency droop known to limit conventional InGaN LEDs. Due to poor conductivity of the outer pGaN shell, current spreading along the entire NR length is challenging and requires an additional cover of transparent conductive oxide in order to fully exploit the active area. At the same time, quantum wells (QWs) on core–shell NRs are grown on m-plane rather than conventional c-plane GaN facets. The calculations show that the absence of piezoelectric fields on these non-polar facets results in strong reabsorption of the emitted photons. A comprehensive numerical model is applied, linking internal quantum efficiency (IQE) and light extraction via the process of photon recycling. In summary, increasing optical absorption and photon recycling losses limit extraction efficiency. While this partially compensates the gain in IQE with increasing active area, a net improvement of the external quantum efficiency (EQE) of +10% is achievable by the proposed design of a novel core–shell NR LED.