We present a thorough analysis of the foundations of models of stabilization of negative capacitance (NC) in a ferroelectric (FE) layer by capacitance matching to a dielectric layer, which claim that the FE is stabilized in a low polarization state without FE polarization switching (non-switching), showing that the concept is fundamentally flawed and unphysical. We also analyze experimental evidence concluding that there is no data supporting the need to invoke such stabilization; rather, conventional models of ferroelectric polarization switching suffice to account for the effects observed. We analyze experimental evidence that at least in some of the model systems for which this effect has been claimed, categorically rule out stabilized non-switching NC. Microscopic measurements recently published as supporting non-switching stabilized NC actually rule them out, since the ferroelectric in a stack sandwiched between two dielectric layers was found to be in a mixed domain state (high polarizations within each domain) rather than in the low polarization state predicted by non-switching stabilized NC models. Nonetheless, since stabilized NC (corresponding to a minimum in free energy) is not physically impossible, it would be useful to move the research efforts to investigating scenarios and systems in which this effect is possible and expected and assess whether they are useful and practical for low power electronics.