A moment of truth is the culmination of countless procedures, processes, and interactions within the business. In the ideal world, the caller (I'll use "caller" generically regardless of the mode of communication) will dial you up, instantly get to an agent who immediately provides the correct response. The ideal is an absolutely frictionless exchange between the caller and the contact center. (The extreme ideal is where customers simply send you money all the time and all the right things magically happen, but we won't get into that.)
In reality, it's unreasonable to expect to have a contact center with an unlimited number of rockstar agents waiting on pins and needles to answer the phone as soon a caller dials in. It turns out that approach is pretty expensive and, actually, unnecessary. As a matter of fact, it can be quite challenging to have the contact center staffed appropriately even when the forecasted volume is rather predictable. Agents don't always make it to work. Traffic, weather, illness, and other factors mean you may have fewer people to help your customers. Surprises like a billing error or un-announced marketing campaign could send call volume through the roof.
It's tough to deliver that moment of truth when the customer has been waiting in queue for 5 or 10 or 30 minutes. Almost nothing the agent does right can recover from the painfully long wait in queue. This is where automated callbacks really shine: the IVR warns the caller of a long wait in queue BUT offers to hold the callers place in line WITHOUT having to stay on the line. The caller may still have to wait, but not have to wait in queue listening to hold music. While perfect staffing conditions is the ideal scenario, using automated callback is a fantastic solution in the real world. Callbacks are easy to use and help to set the stage for the moment of truth.