I'm not to sure about both world wars. Certainly not for the better part of the first one. In documentaries I've watched, German military leadership after WW1 did give much flexibility to all ranks, including the lower ones. Given the very small size of the Reichswehr between the wars and using the during WW1 developed storm trooper tactics it was a necessity and an innovation.
This was unique for the German army, as far as I know no other army did it in this time period.
Between the wars only the very best veterans and later most promising recruits were allowed in the Reichswehr. (A certain lance corporal Adolf H. wasn't, for example.) All ranks were trained to replace their immediate commander and the rank above him. For several reasons:
- Flexibility on the battlefield
- Building up a new cadre for when the Reichswehr would expand
Be aware that the German army from the armistice onwards planned to regain its old size, stature and position. The German army trained (secretly) officers and tactics in the USSR between the wars. The German navy developed (illegally) submarines in Holland and Sweden. Long before this lance corporal H. comes into play. All he actually did was turn the switch from 'covert' to 'full production'.
When that happened, it paid off. Germany reintroduced the draft again in 1935. All existing ranks were bumped up one level. Corporals became sergeants, lieutenants captains, colonels brigadiers, etc. It's very difficult to grow a force of 100.000 man into a force of 3 million, but the Germans did it almost overnight. Not without problems, though. Enough and capable non commissioned officers was always a big problem during WW2.
Over all, the flexibility of the German army was far superior to that of the allies. The Allies won because they out produced Germany in every field. They had far more tanks. More, not better. With the exception of the T 34. Much higher mechanization (most German divisions had horse drawn supply carts), and from mid 1944 total air supremacy. Even so, it took them almost 3 months to fight from the beaches of Normandy to Paris. At a huge cost of life (on both sides). Despite being commanded by a lance corporal making not very sensible decisions, the flexibility of the German army was what it kept going.