Some time ago, I was hired to develop training materials for a large company that was itself contracted to provide training for a healthcare product firm, located in another city. Since we were not all in the same place, a series of conference calls brought me, my direct client, and their client together to manage the project.
When the project manager was delayed for one of these calls, he put an assistant in charge. But in the end, I was the one who knew what was happening, what was needed, and I was the one who really guided the meeting.
After that meeting, and again after another one where the same thing happened, my client explicitly acknowledged that my ability to keep the project going when he wasn't available was a big benefit to them. It wasn't just avoiding a delay. It was that the project manager could have confidence that I would represent his views accurately and professionally to their client in all my interactions with anyone involved in the project.
In other words, the benefit was not just "productivity" or some kind of "output" that had financial ramifications.