We can identify the thoughts that are least valuable to us by observing what our mind goes to when we're bored: mostly, we daydream and retread old lines of thought. That means that when there are worthwhile topics to think about, daydreaming and retreading should be the first things to go.

Have a minor point with your connotations. Do note the limits of introspection. We do not have conscious access to everything that goes on while daydreaming. Since daydreaming, itself, has been linked to problem-solving - not to mention that it's often relaxing and helps you gather your strength before resuming conscious problem-solving - I'm not nearly as certain as you that daydreaming is as useless as you make it sound.