In this article, we analyze power dissipation in the nonadiabatic switching event in mixed-valence (MV) molecular cells of quantum cellular automata (QCA) in combination with a key functional property of cells such as polarizability in the applied electric field. We demonstrate that although the requirements for a strong nonlinear response of the cell to the applied electric field and low heat release are competing from the point of view of molecular parameters, this by no means can be regarded as an insurmountable obstacle for achieving functional advantages and possibility of practical application of QCA. The general theoretical consideration is applied to the series of MV compounds exemplifying electric field-switchable MV molecules, which include oxidized norbornadiene [C7H8]+ (I) and its polycyclic derivatives [C12H12]+ (II), [C17H16]+, (III), [C27H24]+ (IV), and [C32H28]+ (V). Based on the results of high-level ab initio calculations performed for the series of compounds with variable length of the bridge connecting redox groups, we show that strongly localized cation radicals with long bridges can be easily polarized even by a fairly weak electric field. This ensures quite low power dissipation, which is shown to coexist with a rather strong nonlinear cell-cell response. We thus conclude that consideration of the series of MV dimers with controllable electron transfer provides a reasonable way to design molecule-based QCA cells with the required properties.