Development of moral system

There are 6 different levels on the moral system development we go through from our childhood and youth. If we get to reach the last level we become into a full- develope human being and this get us closer to the posibility of living happily
The levels are:
1- Selfishness
Stage1 Punishment. "I will not do this because I don't want to be punished."
Stage2 Reward. "I will do this because I want to be reward."
2-Social approval.
Stage3 Interpersonal relations. "I will not do this because I need people to like me"
Stage4 Social order. "I will not do tis because I would be breaking the law"
3-Abstract ideals
Stage 5 Social contract. "I will not do this because I'm not obiged to do so"
Stage 6 Universal rights. "I will not do this, it's wrong whatever anothers say"

In any moment of our life we can behave in any of this levels but if we usually behave considering the last one is because we have come to a full development of our cognitive skills. We consider the differents variables affecting each situation to consider its morality.
But, why is it so important to be happy to have a 6 level of moral system and good cognitive skills?
Our happiness depends on how we understand the reality, on how we think about everything, to have a good cognitve skills help us to consider the matters from differents points of view, consider alternatives, being objetive, knowing why we make the things and changing our way of doing if necesary, make us flexibility.
Mental skills like everything in our live have to be trainned and the only way of doing this, it's using our brain, thinking.
For example, one moral dilemma: Death penalty. You can take one position about it and explain why. It can be a good moral exercise that train your cognitive skills.

I can say that death penalty is in relation with our consideration of social relations, whether we relation by love or by justice. By justice we consider the revenge like a way of rewardering the victims. Another way of consider social relation is love, consider the posibility of failing and learning from it. In this way it would be the rehabilitation penal system, you consider the criminal like somebody who did something wrong and try to help this person to adapt to society at the same time you protect society from people who can damage anothers.
what do you think?
The moral levels are taking from Lawrence Kohlberg. On the last 50s he was making an experiment. He follow children while turning into adults to know the level of moral development they were going throught and the top they come. I'm sorry I have the information only in a spanish article. (Temas 49 Investigación y Ciencia. Article "El desarrollo moral de los niños" William Damon). But I think it would not be much difficult to find something about it in english searching in internet.