The early steps of photosynthesis involve the photoexcitation of reaction centers (RCs) and light-harvesting (LH) units. Here, we show that the historically overlooked excitonic delocalization across RC and LH pigments results in a redistribution of absorption amplitudes that benefits the absorption cross section of the optical bands associated with the RC of several species. While we prove that this redistribution is robust to the microscopic details of the dephasing between these units in the purple bacterium Rhodospirillum rubrum, we are able to show that the redistribution witnesses a more fragile, but persistent, coherent population dynamics which directs excitations from the LH toward the RC units under incoherent illumination and physiological conditions. Even though the redirection does not seem to affect importantly the overall efficiency in photosynthesis, stochastic optimization allows us to delineate clear guidelines and develop simple analytic expressions in order to amplify the coherent redirection in artificial nanostructures.