I don't think many of us reading this post are the type to think that they can ignore behavior and some day the child with "outgrow" it. I often get questions in person from people of "At what age will my child stop doing XYZ?" This is always in reference to some discipline issue. My response is always the same. I tell people the child will stop doing it when the parent requires the child to stop.
Of course certain things are within reason and natural tenancies of age groups. Toddlers are very self-oriented and require the developmental milestone of growing to think of others (typically starting around age three). Once the child is capable, however, of learning to think of others and develop sympathy and empathy, these desirable qualities will not be developed without effort.
People don't "grow out" of undesirable qualities. They are either taught to live another way, with much effort and practice put into doing so, or they learn "the hard way" through "life's" lessons. A lot of heartache can be saved if we help our children to learn virtues through means other than hard trials in life. Doing so will not eradicate trials from life--trials happen even to the best of people. We all know that. Doing so will simply allow for further growth because the trials will be improving and building on the sympathy, rather than simply teaching it.