Delivery costs roughly the same whether the parcel holds one item or four. Confirmation costs the same call. So a low-priced single-item order can be delivered successfully and still lose money once the failed attempts on other orders are averaged in.
This is why experienced COD sellers push bundles and upsells rather than cheaper products. Raising AOV spreads a fixed cost over a larger sale, and it is usually easier than raising the delivery rate.
AOV on its own is misleading in COD, because it counts orders that were never delivered. The figure that matters is AOV on delivered orders — what actually arrived and was actually paid for.
Very high AOV can also work against you: the larger the amount a buyer must produce in cash at the door, the more likely the order is refused.