I am in the middle of Reimer, Paolitto and Hersh's Promoting Moral Growth from Piaget to Kohlberg as part of research on business ethics.
Kohlberg claims that as children mature they develop greater capacity for ethical deliberation in six stages. The two highest levels are adapted from formal philosophical systems, John Rawls's contractual utilitarianism and Kantian duty-based ethics, that all action should be a universal law to (in Kohlberg's version) maximize social welfare.
Levels five and six make the claim that concern for society at large equals moral maturity. Kohlberg confounds complex thinking with moral maturity. Some people consider social justice in their moral thinking, others may give weight to economic rationality. This does not make strong utilitarianism (the agent's thinking of society at large) more "mature". It just makes it acceptable to Kohlberg and his followers.
In one of the case studies he uses to test moral maturity, Kohlberg excludes economic rationality from moral deliberation. He views people who think that it is moral to steal a needed drug as more moral but those who understand that strong moral assumptions about stealing are necessary for economic rationality are less so. In other words, the advocates of moral maturity see theft as morally acceptable if it maximizes economic illiteracy. Kohlberg's theory is ideologically utilitarian.
Kohlberg claims that moral maturity causes social justice thinking when the relationship ought to be that cognitive eomplexity causes complex ethical deliberation. Numerous grants for ethics programs were awarded to Kohlberg and his followers.