I used to have a job like that, and was expected to be reachable 24/7, even when on vacation.
Customer might have major issues or there might be a hiccup with an outstanding order. Technically we had staff to cover, but it was expected that the larger customers would have a direct way to contact us, so would not sit through a phone tree if a server rack went offline.
Plus my paycheck and my extension my job were dependent on those customers staying happy, so even if I had others to cover for me, if they put my people on the back burner, it'd be me who would have the hit.