The challenge of stopped-down AF is that AF has inherent error, Canon states it as defined by an acceptable range within one DOF zone. When the lens is stopped down, the DOF zone grows and the range of tolerable error widens, reducing the inherent accuracy of the focus achieved!
This illustration shows the principle. Any focus within the zone of AF ambiguity (pink zone) could be 'acceptable' to the camera's AF sensor, yet it is not necessarily focus on the main point of interest where the AF point is aiumed. (note: The DOF 'in focus' should be labelled f/8 DOF 'in focus'.)