No deeper understanding here, just a student like everybody else. Precession is as described, but I need to make some clarifications.

FAA is correct (relief), the DG does not reply on precession to work properly. It relies solely on rigidity in space. It is adversely affected by precession, and must be corrected occasionally using the little knob.

The Attitude Indicator uses rigidity in space to show bank angle, by simply staying put as shown by a fake horizon. As the aircraft rolls it carries the little airplane on the dial into the roll with it, and voila you have bank angle. Pitch indication is accomplished the same way, using rigidity in space.

However, the precession is found to do both "good" and "bad" things to an AI. Good effects are, precession corrects the gyro back to level when it gets tilted by action of the little air valves at the base. "Bad" effects come from the gyro responding to accelerations of the aircraft in erroneous ways momentarily. It precesses in reaction to accelerations placed on it, just as the rate gyro does in the turn coordinator does but this time it is useless information.

In contrast, the Turn Coordinator relies on the "good" kind of precession to do its job, and would not work without precession of that sort. It senses angular acceleration, a fancy term for reaction to the rate of turn of the aircraft around the yaw axis. It also uses rigidity in space. It is technically known as a "rate gyro" because it reacts to rates of turn as well as acceleration (rate of a rate, you could say). That is what prompted me to get fussy about it. Rate gyros are useful because they precess so nicely!