Should teens depend on their parents

As a teenager I grew up depending on my parents. They used to pay for my education, and i used to depend on them for pocket money. And I am sure, that this is the case with most of us in india today. But if you see in west, as far as I understand, most of the teens work and earn on their own. While this has a good side there is a negative side also, some teens who work at their early age loose their direction and may become school dropout or end up landing no where.
Do you think that teens should start work and become independent?