We present a critical assessment of the range of validity of the empirical Cox-Merz rule for a wide range of model entangled polymer samples with a well-defined molecular structure, from linear monodisperse and polydisperse polymers, to branched model polymers (i.e. stars, H-polymers, and combs) and blends of linear polymers of the same chemistry. We focus on melts and concentrated solutions. Overall, we find that the simple empirical rule is obeyed rather well for the investigated cases. As often reported in the literature, relatively small systematic failures occur with the steady viscosity being below the complex one at high rates for most polymers, with linear polydisperse polymers (with a polydispersity index of about 2) being a notable exception. For the latter polymers, the rule is obeyed identically within experimental error. More unusual failures, with the steady shear viscosity being higher than the complex viscosity, are found for branched polymers with more than one branch point. More specifically, these unusual failures are observed at very high branching levels, when the backbone of the polymer is being stretched at low rates due to the motion of the branch points. The extra stress coming for the stretch renders the steady viscosity higher than the complex one. Due to the well-characterized nature of the combs, we can state that failures of the latter type are only apparent when the branches comprise more than 70 % of the molecular structure of the comb. This estimation could serve as a rough guideline in applications, although it is only a necessary and not sufficient condition for these failures to occur.