Saying a 5.9L is THE replacement engine isn't really the most accurate statement. There have been plenty repowered with 8.3's. And in reality, the C series is a closer match to the herc in size and low end torque and is right at home in the tub of a 2-. Plus, since it's running at a lower BMEP, it is a longer lasting engine when at comparable power levels.
The reason the 5.9's are more commonly used for conversions is the shear number of them, number of parts, and the fact they are cheap. The 8.3's are still out there working.
A lot of the reason behind White using a 5.9 was cost. At a time when they were being sucked dry, they were trying to make every penny they could. A rotary pump 5.9 saved White considerable money over the C series with an inline pump used by CaseIH on the Magnums. But, White sacrificed low end torque and longevity as a result.