On some instrument approaches, the autopilot-coupled approach is not authorized or not authorized below a certain minimum. For example,
- Autopilot-coupled NA (MRY: ILS OR LOC RWY 10R)
- Autopilot-coupled NA below a minimum (LVK: ILS RWY 25R)
Moreover, on some approaches, the DA is lower if we have a AP/FD/HUD.
I guess the lower DA is because we can give more attention outside the window when there is AP/FD/HUD's assistance. I didn't come up with any idea or context why autopilot-coupling won't work.
If it is turbulent and the autopilot doesn't respond quickly enough to keep the needle centre, we may not use autopilot at all. If the air is calm, the autopilot may well outperform hand-flying. However, it depends on the quality of the autopilot.