The EDSP is not used in markets that exchange physical assets, for example, the commodities market. The price at which commodities exchange hands on delivery is the original price traded.
However, the EDSP is still used if you are settling the price of an underlying derivative contract on the commodities market. This is because these types of contracts are not settled for physical delivery. In fact, a vast majority of crude oil contracts on NYMEX are cash settled.
Whether the contract is for a financial or physical asset does not affect the need for exchange delivery settlement prices. Exchanges need to use an EDSP to calculate the difference between the traded price and price at expiry.
The EDSP is usually set on the last trading day of a contract, and payment of the difference calculated is usually a day or two thereafter. In the case of a futures or forward contract, the EDSP will be used to determine the last price before expiry.
Stock markets also use exchange delivery settlement prices as they are used in single share futures. Stock exchanges are in charge of determining the EDSP to be used for each share. Plus, the stock exchanges calculate indices that are made up of shares quoted on their exchange.