That's all good and well, if the system is able to accurately define what is causing the problem. If it's not an input error, not a malfunction of the autopilot computer itself, then one is left with other problems that can produce similar results, but which will continue to be a problem should the autopilot degrade to a lesser state of control.
Eliminating the autopilot completely takes all the problems out of the look, returns control to the pilot, and allows the matter to be resolved using a procedure.
Attempting to simply fall back to basic autopilot functions when the issue is a runaway stabilizer trim, for example, may only escalate the problem. Taking autopilot away and allowing the crew to manually fly eliminates the trend, allows the crew to restore equilibrium, and then address the problem.
I agree wholeheartedly that stepping "back into the loop" in turbulent night conditions in the top of a cloud layer or a mountain wave can be a challenge, but then isn't this the reason for having a crew on board in the first place? Fly and control the airplane. Make decisions that the automation cannot. Evaluate. Troubleshoot.
Raw data training these days is often seen as redundant, and in many cases, "raw data" still includes use of the flight director. Crews should be comfortable transitioning between manual flying, and automation, equally proficient in both, and this practice should be approved and encouraged by operators.