Use the credit card. Although it is hefty cash deposit being required, Norwegian has to set a standard policy and they can't fit the deposit amount to individuals based on their saying 'we don't spend that much'. Can you imagine how hard that would be to administer?
I don't know the reason for this high amount. Perhaps Norwegian has been burned by people using cash, or perhaps they are trying to discourage the use of cash deposits since people tend to be more free spending if they use a credit card, and they figure if a large cash deposit is required most guests will use it all up. As with most things, the goal is to make it easy for you to spend the most, one way or another.