Interesting question, never ran across it before.
The one thing that comes to mind is the possibility of the overall diameter being "slightly" different between a "C" and "D" load range tire....... something to confirm.
I don't have enough knowledge on the subject to comment one way or the other..., but I personally prefer to keep my four TT tire specifications/ratings the same.
2016 GM 2500HD 6.0L/4.10
2018 Jay Flight 24RBS
2002 GM 2500HD 6.0L/4:10 (retired)
2005 Jayco Eagle 278FBS (retired)
1999 Jayco Eagle 246FB (retired)
Reese HP Dual Cam (Strait-Line)