I'm not entirely sure of how your question relates to this discussion, but to answer it in the general case... Assuming the elephant is well-trained, then it's usually better for it to be in control. For instance, you'll want to let your elephant handle moving your feet back and forth when walking, instead of needing to consciously think about each step. You want to let your elephant automatically interpret others' facial expressions, instead of having to figure out their meaning yourself, and so forth. Of course, if the elephant is badly trained and e.g. misreads others' expressions, then you should re-train it. But once you've done so, you'll want it to take over again.

The rider is conscious, directed attention which tires quickly. The elephant is automatic processes which run constantly and tire much more slowly. You should train your elephant to take care of as many things as possible, and conserve the rider's energy to only the cases where it's really needed.

Of course, the "should" is kinda redundant here, since you can't avoid doing this. Whenever you repeat some behavior long enough for it to become automatic, you're training the elephant to act in a certain way and then transferring control to it.