Note that the following answer covers all types of ACH and the full gamut of clearing not just the US ACH. remember that ACHs exist for commodities, shares, bonds, derivatives etc. as well as plain cash.
An ACH does things that banks don't and banks don't do what ACH does; communicate. ACH nets and clears assets between financial institutions without being one itself and without the intervention of either of the counterparties. In essence they prevent arguments between financial institutions and prevent money being transferred. They also control when and how any assets to be transferred are transferred.
Netting is the process whereby a period's (normally a day but could be any period) incoming and outgoing transactions for a pair of institutions are compared and only the net amount; the larger value - the smaller value, is transferred. This prevents the need for lots of small transfers throughout the period and prevents assets being unnecessarily transferred.
As communicators they provide a common point of contractual obligation between institutions. If I were a firm that wanted to do business with multiple businesses I would have to have a separate contract with each of them if it weren't for an ACH with whom I can have a contract and my potential correspondents can have a contract. Thus ACH provides a legal buffer between institutions; if my counterparty to my trade reneges on the deal I have the legal force of the contract with the ACH and their legal team to lean on. In many cases the ACH will even insure my against any loss from a counterparty defaulting on an agreement. It will also be harder for a defaulter to do business if they are blacklisted by an ACH for defaulting. The consistency of their contracts also makes communications simpler.
In addition to the benefits of the contracts being standardised and with a centralising intermediary they have the benefit of having standard terms of service to allow planning for cash flow. If I know that a cashflow should occur every month at the same time the ACH will ensure that it does so with predictable rules for what happens if, for example, that date is not a business days some months or doesn't even exist some years (29th of February). The benefit of this knowing how and when the assets I am due will be available and when assets that I need to transfer will be removed.