Free charge generation after photoexcitation of donor or acceptor molecules in organic solar cells generally proceeds via (1) formation of charge transfer states and (2) their dissociation into charge separated states. Research often either focuses on the first component or the combined effect of both processes. Here, we provide evidence that charge transfer state dissociation rather than formation presents a major bottleneck for free charge generation in fullerene-based blends with low energetic offsets between singlet and charge transfer states. We investigate devices based on dilute donor content blends of (fluorinated) ZnPc:C60 and perform density functional theory calculations, device characterization, transient absorption spectroscopy and time-resolved electron paramagnetic resonance measurements. We draw a comprehensive picture of how energies and transitions between singlet, charge transfer, and charge separated states change upon ZnPc fluorination. We find that a significant reduction in photocurrent can be attributed to increasingly inefficient charge transfer state dissociation. With this, our work highlights potential reasons why low offset fullerene systems do not show the high performance of non-fullerene acceptors.