Its not entirely clear to me what that term meant. So much of this does go over my head a bit. But I think they are referring generally to the entire class of cheese, not a specific production method of "Cheddar" cheese.
I'm not sure what the disadvantage of using smaller cubes would be after stirring or cheddaring.
I suppose the whole point of milling the cheese into cubes after cheddaring is to provide sufficient surface area for the salt to adhere to. That said, I would guess there is a balance there between sufficient surface area, and relative (re)-knitting required. The finer the cubes, the more surface area for the salt, but more knitting that will be required. That might have an impact on texture. (I really don't know)
To me, the point of milling is to undo just enough knitting (cheddaring) to increase the surface area to the minimums required for salting. Any "gatuitous" surface area would just undo the gains made by the cheddaring process.
Would a finer cube after milling release more whey?