We present a detailed theoretical analysis of the electronic and optical properties of c-plane InGaN/GaN quantum-well structures with In contents ranging from 5% to 25%. Special attention is paid to the relevance of alloy-induced carrier-localization effects to the “green gap” problem. Studying the localization length and electron-hole overlaps at low and elevated temperatures, we find alloy-induced localization effects are crucial for the accurate description of (In,Ga)N quantum wells across the range of In content studied. However, our calculations show very little change in the localization effects when moving from the blue to the green spectral regime; that is, when the internal quantum efficiency and wall-plug efficiencies reduce sharply, for instance, the in-plane carrier separation due to alloy-induced localization effects changes weakly. We conclude that other effects, such as increased defect densities, are more likely to be the main reason for the green-gap problem. This conclusion is further supported by our finding that the electron localization length is large, when compared with that of holes, and changes little in the In composition range of interest for the green-gap problem. Thus, electrons may become increasingly susceptible to an increased (point) defect density in green emitters and as a consequence the nonradiative-recombination rate may increase.