If we talk in general then kids should first grow up, establish their identity and know what they want in their life before getting married. If they don't know about themselves then how can they be called mature enough to take decisions regarding life long commitments such as marriage? We cant expect them to fall in love at 12-13 and then have 1-2 years to decide if they want to get married or not.
At least, in the context of India, I don't see kids to be mature enough for marriage at that age. Moreover, do we want them to start producing kids starting from that low age?
Another point is about career: In ancient times people didn't need to go to college till 20-22 years of age. Moreover, there was a need to get married quickly and produce children because of low life expectancy due to wars etc.
Do you think that marriage wont hinder anyone's career in today's age?
In fact, if we talk about India then how will we stop people from exploiting that rule?
For example parents might force their kids to get married because it is easy to force people when they are small. Or someone aged (lets say 25 - 30) marrying a 15 year old girl (lets say parents forced her) and dominating her for whole life because of age difference?