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Inorganic perovskite solar cells show excellent thermal stability, but the reported power conversion efficiencies are still lower than for organic-inorganic perovskites. This is mainly caused by lower open-circuit voltages (V(OC)s). Herein, the reasons for the low V-OC in inorganic CsPbI2Br perovskite solar cells are investigated. Intensity-dependent photoluminescence measurements for different layer stacks reveal that n-i-p and p-i-n CsPbI2Br solar cells exhibit a strong mismatch between quasi-Fermi level splitting (QFLS) and V-OC. Specifically, the CsPbI2Br p-i-n perovskite solar cell has a QFLS-e center dot V-OC mismatch of 179 meV, compared with 11 meV for a reference cell with an organic-inorganic perovskite of similar bandgap. On the other hand, this study shows that the CsPbI2Br films with a bandgap of 1.9 eV have a very low defect density, resulting in an efficiency potential of 20.3% with a MeO-2PACz hole-transporting layer and 20.8% on compact TiO2. Using ultraviolet photoelectron spectroscopy measurements, energy level misalignment is identified as a possible reason for the QFLS-e center dot V-OC mismatch and strategies for overcoming this V-OC limitation are discussed. This work highlights the need to control the interfacial energetics in inorganic perovskite solar cells, but also gives promise for high efficiencies once this issue is resolved.