The strict WignerWitmer symmetry constraints on chemical bonding are shown to determine the accuracy of electronegativity equalization (ENE) to a high degree. Bonding models employing the electronic chemical potential, mu, as the negative of the ground-state electronegativity, chi(GS), frequently collide with the Wigner-Witmer laws in molecule formation. The violations are presented as the root of the substantially disturbing lack of chemical potential equalization (CPE) in diatomic molecules. For the operational chemical potential, mu(op), the relative deviations from CPE fall between -31% <= delta mu(op) <= +70%. Conceptual density functional theory (cDFT) cannot claim to have operationally (not to mention, rigorously) proven and unified the CPE and ENE principles. The solution to this limitation of cDFT and the symmetry violations is found in substituting mu(op) (i) by Mullikens valence-state electronegativity, chi(M), for atoms and (ii) its new generalization, the valence-pair-affinity, alpha(VP), for diatomic molecules. Mullikens ?M is equalized into the alpha(VP) of the bond, and the accuracy of ENE is orders of magnitude better than that of CPE using mu(op). A paradigm shift replacing the dominance of ground states by emphasizing valence states seems to be in order for conceptual DFT.