It is a great thing to have, however, if enough people took advantage of this, we would not have as many liberties as we do today. We could loose any social club someone didn't agree with, even the philanthropic organizations could take a severe beating. They learn to be honest when their parents deal with them honestly. They learn to be responsible when their parents provide for them and keep them safe. Apologizing is important not only as a teaching tool for children, but also for parents who tend to beat themselves up for their own mistakes.
Children tend to be far more forgiving than their moms or dads.
Apologizing to kids after making a mistake is part of being a good role model. Parents care for them, feed them, give them a place to stay and meet their needs and wants to the fullest of their ability. Parents stay awake many hours of the night taking care of their children and making sure they are all right. Children, when young, believe that their parents are their best friend. This does not hold true for most teenagers.