Which restrictions?
Well, a corps might order one division to give a Bde to another Div, but then you're again at a higher span of command for the latter division (and the div/bde staffs don't know each other). Keeping brigades under command of a specific division ties them together. You get bundles of brigades which you couldn't move as freely in a corps sector as you could without the division layer. That's one restriction.

A corps HQ has a picture of the corps area, issues missions to division HQs which in turn update their own intent and issue orders to brigades.
The lag in here should be obvious. Such a lag is a restriction on agility of command.


I'm not particularly interested in DS or OIF experiences. That's like boxing experiences based on punching ball training. The fact that there were problems at all is embarrassing. A competent army would have created very different challenges and a modern army structure should not be modelled with the least problematic and long since gone opfor in mind.
Yet, if OIF was of interest; the British 1 Armoured Division wasn't an effective HQ in that operation. It issued few orders, and those came often very late. The brigades pulled their weight.


By the way; the quotation marks (" ") are not for paraphrasing. Your third quote was paraphrasing and I would appreciate not to see false quotes.

I can assure you that nobody in the 50's thought of "synchronizing", for that is a much newer fashion - and mostly an anglophone fashion. There's an official military history book on the early years of the Heer (up to 1970) and it clearly tells us that the reason for the division in the second army structure was a political one. The German experts were advocating a brigade-centric army. The result was the Division 59, an often-copied structure which focused on the brigades and left only a small role for the division.