We need the law to protect vulnerable young people from those who have no respect for the law, what anyone says or any social restraint. To think being told will do is naive.
Your point about the age of consent being a sudden permission to have sex - I just don't believe that youngsters work that way - marking off the days to when they can rush out one morning and have sex. I think protection is more important.
By stigma coming from social aspects I mean it is culturally driven through local expectations, or religion. The law is free from prejudice in this and supersedes culture. What might be a practice in Hindu culture - marrying children at 12 - becomes illegal.