Applying extensively excess ammonium halides in forming perovskites is a widely used approach to achieve high-performance perovskite light-emitting diodes (PeLEDs). However, most of these PeLEDs suffer from severe external quantum efficiency (EQE) roll-off at high current densities, thereby restricting the realization of high-brightness PeLEDs and laser diodes. In this work, we explore the underlying mechanism of the EQE roll-off in high-efficiency formamidinium lead iodide (FAPbI3)-based PeLEDs. By combining voltage-dependent electrical stress measurements and ex situ ion distribution analysis of PeLEDs, we found that the electric field-driven migration and local segregation of excess iodide ions, originated from nonstoichiometric precursors, trigger the EQE roll-off via promoting imbalanced charge injection. Based on this discovery, we introduced a simple wash-off treatment with chloroform to remove the excess iodides from the perovskite surface and demonstrated that the treatment is highly effective in suppressing the roll-off behavior. By combining the treatment and the use of an ultrathin poly(methyl methacrylate) (PMMA) interlayer, we achieved a high-brightness PeLED with an EQEmax of 19.6%, a critical current density of 1550 mA cm-2, and a radiancemax of 875 W sr-1 m-2. The study reveals the double-edge sword effect of precursor nonstoichiometry and highlights the importance of managing excess ions in perovskite films.