Because Cash On Delivery is an optional service for most carriers, which they charge for, you will be cutting into your profit margin by using it.
Canada Post for example charges $7.25 for COD, since their carrier has to wait for the recipient to answer the door, find her purse and pay, then has to keep track of the payment.
And it won't be cash, it will be an electronic payment that you pay fees to receive.
And why would a customer demand it?
Most people are used to paying at the time of ordering and COD is mostly used by "real" businesses when they have a customer who is not good about paying bills. It's a Seller Protection against deadbeats.
The industry Best Practice is take order, get paid, ship.
Never ship before you are paid.
Also dropshipping is a mug's game. While the suppler gives you the pictures and description, packages the product and ships it, you have no control over any of those things. But if the customer is unhappy with her purchase, you take all the responsibility. Which means refunding because you can refuse returns, but you cannot refuse refunds.
