The possibility of a III-nitride LED with 100% or greater wall-plug efficiency is examined considering recent observations of the phenomenon for smaller bandgap mid-IR LEDs under extremely low-bias operation \[Phys. Rev. Lett. 108, 1 (2012)\]. Thermoelectric pumping of carriers by lattice heat enables $\geq$ 100% WPE, but this effect is relatively weaker for the wider band gap III-nitrides. This work assesses the electrical and optical performance of several state-of-the-art nitride devices and summarizes the requirements and prospects for approaching $\geq$ 100% WPE for III-nitride LEDs operating at technologically relevant current densities (> 1 A/cm2).