Why get accidental death insurance when you have a life policy?
You may or may not actually need another life insurance policy for accidental death, but it is true that the more insurance you buy, the more money your dependents will receive in the event of your death. Of course, it is also true that the more insurance you buy, the more it will cost you in premium payments, and if you do not suffer an accidental death, you will never receive anything for that money. So, it's a kind of gamble. Your dependents might come out ahead, or they might not.