Well I can agree with you on the traveler not completely being a "living thing." And if I'm not mistaken I believe the speaker says the traveler starts to regain light after we stop the ritual that the hive were performing on a shard of the traveler. The reason we destroy the black garden is because we are lead to believe that the vex are controlling it and want to destroy every planet and turn them into their machines. So we killed the heart in order to stop the vex and protect the last city. Not so the traveler could begin to regain it's light since it had already started doing that when we stopped the ritual of the hive.