Indeed, what saved the Entente in World War 1 was the fact that Belgium, which had been expected to roll over and allow the German army unmolested free passage, actually called up its military and fought. That ruined the German timetables, allowing France to complete its mobilization and brought the British into the war preventing a quick German victory on the Western Front.
Towards the end of the war, yes, Germany was beginning to move towards what we would consider a "commander's intent"-based system. Erwin Rommel's text, Infantry Attacks, captures this transition. However, it's inaccurate to say that the German military was any less rigid than the British.
It is also inaccurate to say that the death rates of the German army were any less than they were for the British. Perhaps in 1914 and 1915, as well-trained German regulars were facing off against the "Pals Brigades", the Germans inflicted more casualties than they received. But by the end of the war, as the German economy was crumbling and the prospect of US involvement made the German generals desperate, they resorted to mass infantry charges with relatively untrained soldiers, and took extremely heavy casualties as a result.
If anything, your description of the German army is more accurate for the Wehrmacht in World War 2 than it is for the Kaiser's army.
"As Table 32 shows, the greatest of all the paradoxes of the First World War is that, despite being disastrously disadvantaged in economic terms, the Central Powers were far more successful in inflicting death on their enemies. According to the best available totals for wartime military deaths, some 5.4 million men fighting for the Entente powers and their allies lost their lives, the overwhelming majority of them killed by the enemy. The equivalent total for the Central Powers is just over 4 million. The Central Powers' superiority in killing was thus of the order of 35 per cent. The official British statistics published shortly after the war give an even higher margin of 50 per cent, as do the figures in a number of modern textbooks.52 In other words, the Central Powers were at least a third better at mass slaughter." pg 294
"The trouble was - and here the excuses must stop - that the entire culture of the British regular army militated against effective improvisation. The command structure was based on obedience to superiors and suspicion of subordinates; men could still advance according to their connections; and commanders could still be 'unstuck' by personal quarrels.83 This could have serious repercussions: when Haig questioned Rawlinson's original Somme plan, the latter felt unable to stand his ground, with the result that Haig was able to insist on the suicidal breakthrough objective. As Rawlinson said, 'It is a gamble to go for an unlimited offensive but D. H. wants it and I am prepared to undertake anything within reason [sic].'84 An Army Commander did not presume to correct the Commander-in-Chief, even when tens of thousands of men's lives were at stake.85 Similar inhibitions existed at every level. Orders were issued at the top and fed down the line; there was little traffic in the other direction. As a result, officers, NCOs and men grew accustomed to 'waiting for orders'. In battle, as J. M. Bourne has remarked, 'when German shelling interrupted communications paralysis set in'. To adapt the not inappropriate language of industrial organization, this was 'line management', and it provided no mechanism by which the views of 'junior line managers' could be relayed back to head office.86 Partly for this reason, the proponents of a more technocratic approach made slow headway against the traditional believers in war as a moral rather than material contest.87 Too much emphasis was placed on morale, courage and discipline; not enough on fire-power and tactics." pg 305
"These German tactical strengths were rooted in a distinctive military culture. According to Dupuy, the German military establishment had 'discovered the secret of institutionalizing military excellence'.109 Martin Samuels likewise points to a distinctively German philosophy of combat, which acknowledged its fundamentally chaotic character.'10 This in turn influenced the way command structures evolved. The Germans favoured 'directive command' (task-oriented and decentralized decision making, flexible at all levels) whereas the British preferred 'restrictive control', which deliberately discouraged initiative."1 Differences in training also followed logically from this. German 'chaos theory' demanded a high level of training to promote adaptability; the British approach required only obedience. Moreover, the German officer did not stop learning on obtaining his commission; the officer corps was meritocratic, and dud officers were ruthlessly weeded out."2 This line of argument has been further developed by the work of Gudmundsson on stormtroop tactics, which (he argues) depended for their success on the existence of a 'self-educating officer corps'."3 pg 309
If that's not enough, there's plenty more backup in the book. It's a good read, I recommend it.
If the advice you just gave is so good, why couldn't you (or the book's author) have found an example in which the side following the advice actually won the war?
As for WW1, Germany did defeat Russia. It took America's entry into the war to defeat Germany.
But you want an example. Take WW2. When Hitler allowed his generals to run things, things went well for the German army. When Hitler decided he knew better, he micromanaged the Wehrmacht into defeat and ruin. The Luftwaffe's problems were greatly impeded by Goering making a hash of things, despite his officers pleading with him. Goering would dictate tactics that negated the advantages of the Me-109s in the Battle of Britain. Goering also infamously ordered a literal decimation of his pilots for cowardice, an order that was quietly ignored.
In the naval war, the U-Boot commanders knew that Enigma had been broken and tactics had to change, but Admiral Doenitz knew better and sent them to their doom. Some histories assert that the Germans were clueless about Enigma, but the U-Boot commanders knew the truth.
Totally government run in the case of the military, and healthcare is the most heavily regulated industry (by far) in the US. Heavy bureaucratic regulations make an organization unable to adapt to local and/or changing circumstances.
I read in the book "The Pity of War" by Ferguson that the reason the death rates of the German army in WW1 were so much lower than that of the British is the British generals would craft detailed orders on how the soldiers were to achieve objectives. The German generals would instead just give the officers the objectives. The officers were free to adapt to local circumstances.
A similar idea is a story I heard where a class of new lieutenants were asked how would they go about raising a flagpole. The lieutenants all wrote down detailed instructions and procedures. The instructor said you're all wrong. The correct answer is "sergeant, get that flagpole up!".