Army Group strategy was most effectively utilised by the Germans, witness the creations of Rupprecht, Albrecht, Kronprinz and Luitpold commands (also the fact all these nominal controllers were Royal Crown Princes).
This was not the case in 1914 although it became the German norm later. I suggest that the failure of the German General Staff to create high-level intermediate HQ's during peacetime contributed to the events in August-October 1914, particularly on the Western Front. Forcing senior army commanders to wear two hats; that of commanding their own armies in addition to others was inherently unsatisfactory and proved counter-productive in action.
I understand the German Staff system but the canard that the army commander was a mere figurehead is, in my opinion vastly overstated and unsupported by any more than anecdotal and highly subjective evidence coupled with constant repetition of same. A strong Chief of Staff could certainly save a weak army commander but there is no evidence that a poor CoS would automatically debilitate a strong army commander and there were certainly under-performing CoS out there. That which the German's titled CoS would often wield power and authority of de facto commanders in chief, von Molkte the Younger in 1914 Chief of the General Staff for example but a CoS limited himself to logistical and administrative functions could still be a great asset to a competent commander at any level.
In the German system, staff officers could be delegated tremendous authority but at the end of the day, the entire responsibility for the actions of the CoS still belonged to the commander.
The legal authority and responsibility for command rested with the appointed Army Commanders not the CoS. All of the examples cited demonstrate the facility within the German Army for self-examination and improvement but Lossburg, Bruchmuller and Hentsch (and others more anonymous) were tasked with specific duties and mostly authorised to submit recommendations to the commanders for approval. Staff officers were certainly given authority to act in some situations but it was never uniform or universal. Otherwise there would have been no chain of command and the results would have been chaos. A CoS acted alone with authority that they were given from the titular commanders and in very specific situations; such authority was never automatically implicit in the duties of a CoS at any level.