There are various important social benefits of commodity trading even just on paper. The main ones are risk management, hedging, providing liquidity and secondary market, and price discovery.
For example, both producers and customers of commodities can use future market to hedge risks of adverse price movement. For example, in market for potatoes the potato store always faces risk that the price of potatoes will increase and conversely the potato farmer faces risk that the price will drop. This could be for example due to unpredictable weather patterns which can cause supply to vary from year to year.
One way how to avoid sudden price swings to make a future contract between farmer and seller of potatoes where the farmer agrees to deliver seller certain quantity of potatoes at per-specified price. However, pricing such future contract requires lot of skill and speculation that most farmers or potato store owners might not have so naturally through division of labor this part of work is outsourced to commodity trader. Esentially - your question is in its spirit the same question as what store adds to the market and why sellers exist and why commodity producers just dont sell directly to consumers and again answer would be division of labor as farmer might not necessary be good seller.
Moreover, most traders dont trade just in one commodity but in multiple so it is easier for them to manage risk associated with the trading the commodities, and it is always socially optimal that the party which has the least costs of managing risks takes the risk from parties which have the higher costs of managing risks.
Furthermore, the traders can also provide liquidity to the market. Again a bank or big financial company will certainly have a comparative advantage to the farmer or store when it comes to providing liquidity to the market and this function is connected to the above mentioned function of hedging and risk management so it makes sense that instead of farmers and stores keeping extra liquidity they outsource this task to the commodity trader.
Having a secondary market where you can sell your commodity is another good thing. For example imagine that potato farmer entered into a contract to sell a certain quantity of potatoes at a certain price. However, later one of the parties wants to back out. They can do so by selling the contract on the commodities exchange. Since the exchange is the counterparty to everybody, the farmer may not even know that the buyer has been changed and vice versa (also note that in some textbooks this is also mentioned as a part of market providing liquidity, but in others the provision of liquidity was used in more narrow sense of providing leverage to the market participants).
Price discovery is another important reason why especially spot markets exists. Especially for very highly perishable commodities it might be very hard for farmer or store to know exactly how to price the goods and hence even before advent of modern finance sent some representatives to market to haggle the price for them in one place so they dont need to leave their work to do that (That farmers do this is even mentioned in Plato's republic - so really spot markets existed even in ancient times albeit in less sophisticated form).