We find the recently developed strongly constrained and appropriately normed (SCAN) functional, now widely used in calculations of many materials, is not able to reliably describe the properties of deep defects and small polarons in a set of wide-bandgap semiconductors and insulators $(\mathrm{ZnO}, \mathrm{ZnSe}, \mathrm{GaN}, {\mathrm{Ga}}_{2}{\mathrm{O}}_{3}, \text{and} \mathrm{NaF})$. By comparing first-principles calculations using the SCAN functional against established experimental information and first-principles calculations using a hybrid functional, we find that the SCAN functional systematically underestimates the magnitude of the structural distortions at deep defects and tends to delocalize the charge density of these defect states.