Accepting responisibilities can help teenagers retain good relationship(s) with their parent(s) because it allows the parent(s) to see that their child is able to be independent. This can relieve some stress on the parent(s) part in terms of providing for their adolescent child.
Another reason why it can improve the relationship is because accepting responsibilities means you are much more reliant/trustworthy. This may come in handy for the future if the parent(s) require their child's assistance. They can comfortably instill faith without doubt because their child is responsible.