HfO2-based ferroelectrics have dramatically changed the application perspectives of polarization-switching materials for information processing and storage. Their CMOS compatibility and preservation of high reversible polarization down to a few nanometer thickness make them attractive for various device concepts including non-volatile memories and negative-capacitance-enhanced steep-slope transistors. In the context of these applications, the long-standing discussion of intrinsic (thermodynamic) or extrinsic nuclei-limited switching (NLS) in ferroelectrics has recently gained importance. In particular, the negative capacitance effect that is formally described by the Landau-Ginzburg-Devonshire formalism implies the intrinsic polarization switching driven by the thermodynamic coercive field. On the other hand, recent studies reported the nucleation-limited extrinsic switching, which does not result in the hysteresis-free negative capacitance effect. Here, we analyze the polarization response in the nanometer scale on the ferroelectric/dielectric bilayer where the negative capacitance has been previously demonstrated. Our analysis of the two limiting cases of quasi-static switching and the earlier reported ultra-fast polarization response supports the intrinsic polarization reversal scenario. The compatibility of this mechanism with the previously reported NLS region-by-region switching with remarkably low domain wall velocity is addressed. Our results confirm the usability of CMOS-compatible polycrystalline HZO ferroelectric films for gates operating in the negative-capacitance regime. Furthermore, they point towards possible solutions for optimizing their switching properties for applications including memories.