Winning World War II, Combined Arms Operations

WWII broke out in September 1939 with Hitler's invasion of Poland.  From there, going on til 1942, the Germans' won every battle.  They crushed Poland, Holland, Belgium, Denmark, Norway, Yugoslavia, Greece,and finally France.  They drove the British into the sea at Dunkirk. 
   What accounts for the amazing German combat power?  Answer: combined arms.  German attacks had tanks as the spearhead, with the infantry right behind them.  They had artillery support and air support.
This is effective as all getout.
   It took the Anglo Americans three years to catch on and launch their own combined arms attacks.  It's tricky.  For something real simple, just order an infantry battalion, about 1000 men, to attack somewhere.  This is straight forward, you pass the word to the colonel of the battalion.  Where, when, and that's it.  Now lets add artillery support.  You have to get the guns moved up into range, get the ammunition (heavy stuff that) moved up and the guns emplaced.  Then you have to coordinate so that the artillery knows where and when the infantry will attack.  You want the enemy's front lines shelled just before the infantry moves up, but not too early, shelling tells the enemy that an attach is coming and all chance of surprise is lost. And you want the barrage lifted just before your troops get there. You want the enemy head quarters shelled, you want enemy artillery batteries shelled, and you DON'T want your infantry shelled as they press the attack. You need to make sure the artillery and the infantry are using the SAME maps, with the same names and numbers for terrain features.  You want to have artillery forward observers, with radios, with the infantry so they can let the artillery know when the infantry falls behind the schedule.  All this is complicated. 
   Then if you have tanks, you want the tanks to lead the attack, at least as long as the terrain allows the tanks to pass.  Tanks are maneuverable, but they cannot climb roadless hills, cross swamps, or climb vertical cliffs. Takes more coordination to get the tanks to show up at the right place and do what is necessary.
   Even trickier is arranging for close air support.   Step one is to avoid fratricide.  Your ground units need to be distinct from the enemy's units lest the Airedales bomb your own men.  More coordination.  Get anything wrong and lots of bad stuff can happen.
   It took the Anglo Americans about a year of fighting Germans in North Africa to get all this straight.