The ubiquitous coexistence of the redox cofactors NADH and NADPH is widely considered to facilitate an efficient operation of cellular redox metabolism. However, it remains unclear what shapes the NAD(P)H specificity of specific redox reactions. Here, we present a computational framework to analyze the effect of redox cofactor swaps on the maximal thermodynamic potential of a metabolic network and use it to investigate key aspects of redox cofactor redundancy in Escherichia coli. As one major result, our analysis suggests that evolved NAD(P)H specificities are largely shaped by metabolic network structure and associated thermodynamic constraints enabling thermodynamic driving forces that are close or even identical to the theoretical optimum and significantly higher compared to random specificities. Furthermore, while redundancy of NAD(P)H is clearly beneficial for thermodynamic driving forces, a third redox cofactor would require a low standard redox potential to be advantageous. Our approach also predicts trends of redox-cofactor concentration ratios and could facilitate the design of optimal redox cofactor specificities.