Doped organic semiconductors are critical to emerging device applications, including thermoelectrics, bioelectronics, and neuromorphic computing devices. It is commonly assumed that low conductivities in these materials result primarily from charge trapping by the Coulomb potentials of the dopant counter-ions. Here, we present a combined experimental and theoretical study rebutting this belief. Using a newly developed doping technique, we find the conductivity of several classes of high-mobility conjugated polymers to be strongly correlated with paracrystalline disorder but poorly correlated with ionic size, suggesting that Coulomb traps do not limit transport. A general model for interacting electrons in highly doped polymers is proposed and carefully parameterized against atomistic calculations, enabling the calculation of electrical conductivity within the framework of transient localisation theory. Theoretical calculations are in excellent agreement with experimental data, providing insights into the disordered-limited nature of charge transport and suggesting new strategies to further improve conductivities.