Organic solar cells utilize an energy-level offset to generate free charge carriers. Although a very small energy-level offset increases the open-circuit voltage, it remains unclear how exactly charge generation is affected. Here we investigate organic solar cell blends with highest occupied molecular orbital energy-level offsets (∆EHOMO) between the donor and acceptor that range from 0 to 300 meV. We demonstrate that exciton quenching at a negligible ∆EHOMO takes place on timescales that approach the exciton lifetime of the pristine materials, which drastically limits the external quantum efficiency. We quantitatively describe this finding via the Boltzmann stationary-state equilibrium between charge-transfer states and excitons and further reveal a long exciton lifetime to be decisive in maintaining an efficient charge generation at a negligible ∆EHOMO. Moreover, the Boltzmann equilibrium quantitatively describes the major reduction in non-radiative voltage losses at a very small ∆EHOMO. Ultimately, highly luminescent near-infrared emitters with very long exciton lifetimes are suggested to enable highly efficient organic solar cells.