Here, we capture the consequences of solvent-mediated nonelectrostatic ion-ion interactions, coupled with the considerations of finite-sized effects of the ionic species, on electrokinetic transport in narrow fluidic confinements. We consider pressure-driven flow in microchannels and nanochannels in the presence of electrical double layer effects and analyze the establishment of a streaming potential as mediated by a Yukawa-like pair potential that integrates the ion specificity with the governing nonelectrostatic interactions. We bring out the influences of these interactions on electroviscous effects manifested due to the establishment of the streaming potential. Our considerations provide a plausible explanation for the gross overestimation of electrokinetic energy conversion efficiencies as predicted by classical electrical double layer theories that ignore nonelectrostatic interactions between the ionic species.