I’m wondering what is the wiser course of action in the opinion of experienced animators. Suppose I am moving a whole rigged person walking around a room, do you move the whole rig by moving it in object mode, or do you move the root bone around the room while keeping the rig stationary as an object? It seems to me that although moving the root bone means I don’t disturb IK target bones, the cost is the whole thing ends up wandering further and further from the origin of the object which doesn’t seem right somehow and I suspect is storing up problems for later.
For me the opposite has been my experience. Whenever I’ve moved the rig object (especially with linked groups) I run into trouble. Leave it at the scene centre and move the root, or whatever else you need to get things moving (e.g. hips + ik feed).
Take an analytical look at some well made television, animations or movies. You’ll rarely see someone walking around a room as a single shot. Each time you switch to a new camera you can move your objects to a new location that makes more sense for that shot.
But Blender has no problems keeping track of offsets from the origin. It’s just numbers. It doesn’t matter what the numbers are.