Anecdotally, it seems like the most common cause of alternator failure is a broken field wire at the crimp to the ring terminal where it attaches to the alternator. I have added strain relief to mine and also inspect it every time the cowling is off.
The differences in voltage engine on and off are interesting and worth exploring to better understand. At first look, it doesn't make a lot of sense that the alternator could be the cause. First the field is the rotor and so with no voltage applied, the rotor doesn't do much except spin around. Unlike generators, alternator fields have very little residual magnetism when unpowered. The stator output is connected to the ALT breaker through diodes so current should not flow in reverse. You could verify this if you could pull the ALT breaker, but yours isn't the push on-pull off type (This is probably because the designer never thought there would be a reason to pull it. The breaker has a higher rating than the alternator output and it's purpose is to protect the wire to the alternator from excessive current from the battery should there be a short circuit).
I might fly around long enough so that the battery is fully charged and then land and note the voltage, and then pull the field breaker and not the voltage, and then shut down the engine without turning anything off and note the voltage again to see if it is reproduceable.