Whether to have a credit or debit card or both is for many people a matter of convenience. The fees charged are the costs of having that convenience available and are no different in concept to any other cost for service that would be implicit or explicit in the purchase price of any good or service.
As is often the case, it pays to shop around to get the deal that best suits your needs. For example, neither our bank nor our credit card company charge annual fees for the debit or credit cards. The debit card purchases are deducted immediately from our checking account, so there are no interest charges applicable. We generally pay off the credit card bill in full, so there are no interest charges there either.
Having and using credit or debit cards prudently can and does contribute to your credit score that can reap benefits that far outweigh the cost of owning one of these pieces of plastic. Banks and other lenders will adjust terms and conditions of loans based on your credit score and this can add up to hundreds or even thousands of dollars over the term of loans for high-ticket purchases.
That's my two cents, in credit not cash.