Flexibility
It's clear that out-of-home delivery such as store pickup is more flexible than common home delivery methods. It allows the customers to decide and arrange their time to pay and get the items they want actively, instead of having to stay at home waiting for delivery.
The in-store pickup also surpasses traditional shopping activities at physical stores. Although they both require buyers to come to the store location, the customers choosing cash on pickup don't have to worry about "out-of-stock" (since the order was placed previously) and save the time of walking around to find the products.
Variety
Most buyers love shopping at the stores that provide them with a variety of choices, even when there are some options they will never take.
Due to that, if your e-business can offer from online payment methods (e.g.: credit/ debit cards, e-wallets, and bank transfers) to offline ones (check/ money order, cash on delivery, and cash on pickup), your target customers can choose you over your competitors.