We investigate the capabilities of the mid-infrared instrument (MIRI) of JWST to advance our knowledge of active galactic nucleus (AGN) dust using the spectral fitting technique on an AGN collection of 21 nearby ($z<0.05$) AGN (7 type-1 and 14 type-2) observations obtained with the medium resolution spectroscopy (MRS) mode. This collection includes publicly available AGN and data from the collaboration of Galactic Activity, Torus, and Outflow Survey (GATOS). We developed a tool named MRSPSFisol that decomposes MRS cubes into point-like and extended contributions. We found statistically good fits for 12 targets with current AGN dust models. The model that provides good fits ($\rm {\chi ^2/dof< 2}$) for these 12 targets assumes a combination of clumpy and smooth distribution of dust in a flare-disc geometry where the dust grain size is a free parameter. Still, two and one AGN statistically prefer the disc $+$ wind and the classical clumpy torus model, respectively. However, the currently available models fail to reproduce 40 per cent of the targets, likely due to the extreme silicate features not well reproduced by the models and signatures of water-ice and aliphatic hydrocarbon absorption features in most targets. New models exploring, for instance, new chemistry, are needed to explain the complexity of AGN dust continuum emission observed by JWST.