It has been demonstrated that p-doped polymer layers are a convenient replacement as hole transport layer (HTL) for the widely used Poly(3,4-ethylenedioxythiophene)-poly(styrenesulfonate) (PEDOT:PSS), yielding comparable photodetection performances at low light intensities. In this work, we aim to evaluate the response of organic photodetectors (OPDs) with increasing light intensity when p-doped PBDTTT-c is used as HTL. Photocurrent linearity measurements are performed on devices processed with both PEDOT:PSS and p-doped PBDTTT-c to better determine the role of the HTL. We show a deviation of the photocurrent from linearity for light intensities above 10^-3 W/cm² at 0 V applied bias due to distinct mechanisms depending on the HTL material. While space charge limited photocurrent (SCLP) explains the non-linearity at high light intensity for the device processed with PEDOT:PSS, bimolecular recombination is responsible for the loss in linearity when p-doped PBDTTT-c is used as HTL. The replacement of PEDOT:PSS by p-doped PBDTTT-c, which is 6 orders of magnitude less conductive, induces Langevin recombination, causing photocurrent non-linearity. Therefore, this study emphasizes the need for highly conductive transport layers when photodetection applications are targeted, and motivates further improvements in organic semiconductor doping.