Indium phosphide is the leading material for commercial applications of colloidal quantum dots. To date, however, the community has failed to achieve successful operation under strong excitation conditions, contrasting sharply with other materials. Here, we report unusual photophysics of state-of-the-art InP-based quantum dots, which makes them unattractive as a laser gain material despite a near-unity quantum yield. A combination of ensemble-based time-resolved spectroscopy over timescales from femtoseconds to microseconds and single-quantum-dot spectroscopy reveals ultrafast trapping of hot charge carriers. This process reduces the achievable population inversion and limits light amplification for lasing applications. However, it does not quench fluorescence. Instead, trapped carriers can recombine radiatively, leading to delayed—but bright—fluorescence. Single-quantum-dot experiments confirm the direct link between hot-carrier trapping and delayed fluorescence. Hot-carrier trapping thus explains why the latest generation of InP-based quantum dots struggle to support optical gain, although the quantum yield is near unity for low-intensity applications. Comparison with other popular quantum-dot materials—CdSe, Pb–halide perovskites, and CuInS₂—indicate that the hot-carrier dynamics observed are unique to InP.