Any old group of troops can be thrown together and called a division. A combat-capable division is specialized creature. Like any living thing, a division requires the availability of certain nutrients. A division headquarters contains certain specialists without whom the operations of the division are negatively affected entirely out of proportion to the numbers of the specialists. In WW2, it took the US Army a year to build a new division from scratch, while the component regiments required a fraction of that time.
That much being said, I agree with Leg that niceties of TO&E go out the window once the mushroom clouds start forming. A two-star or senior one-star gets put in charge and is handed an inadequate bag of C3I troops with the instructions to make the godamned best of it. Perhaps some of the corps-level C3I folks are reassigned to the new division. In any event, we are talking about a world war leading to a nuclear war. Despite the tendency of peacetime militaries to demand that circumstances adapt to military bureaucracy, once the balloon goes up reality intervenes quickly.
There is another good reason not to have a basket of separate combat brigades reporting directly to a corps headquarters. Commanders can only juggle so many balls effectively. Napoleon's armies enjoyed many of their early triumphs because he instituted the division level of command; he had subordinate commanders controlling brigade-sized units instead of managing them all himself or creating a number of ad hoc and differently sized commands. The same rules apply today.
Webstral
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