Physical commodities cannot be delivered instantaneously, additionally there is no giant warehouse at the commodity exchange that stores the commodities. This means that what you are going to trade is a delivery contract.

If you play a game like Prosperous Universe, there is no delivery problem on the central commodity exchanges and the commodity exchange has infinite storage capacity. When you buy something, you instantly receive the commodity.

If you want to know why there are duration differences on the contract beyond the delivery itself, e.g. why someone would issue the contract 3 months or 6 months before delivery, then the reason is that they want to minimize income fluctuations or to pay off specific contracts. Similar to how businesses want to turn capex into opex at exactly the rate the money comes in, but this time the goal is for the income to arrive at the same time as the expenses.