Recent JWST observations of the Type Ia supernova (SN Ia) 2021aefx in the nebular phase have paved the way for late-time studies covering the full optical to mid-infrared (MIR) wavelength range, and with it the hope to better constrain SN Ia explosion mechanisms. We investigate whether public SN Ia models covering a broad range of progenitor scenarios and explosion mechanisms can reproduce the full optical-MIR spectrum of SN 2021aefx at ∼ 270 days post explosion. We performed 1D steady-state nonlocal thermodynamic equilibrium simulations with the radiative-transfer code CMFGEN, and compared the predicted spectra to SN 2021aefx. Taken as a whole, the models can explain the main features of this SN over the full wavelength range. However, no single model emerges as a preferred match. We discuss possible causes for the mismatch of the models, including ejecta asymmetries and ionisation effects. Our models suggest that key physical ingredients are missing from either the explosion models, or the radiative-transfer post-processing, or both. Nonetheless, they also show the potential of the near-and MIR to uncover new spectroscopic diagnostics of SN Ia explosion mechanisms.