Weren't the Germans of the late 30s-early 40s really the creators of the concept of combined arms warfare?
Kind of yes, kind of no.
The coordination of all arms in some sort of synergistic fashion was around before armored warfare. For example, the close coordination of infantry, support weapons, and artillery was one aspect of the solution to the geometric increase in firepower before the First World War - a solution that every army in the world had worked out, even if it was awfully difficult to put it into practice. They didn't have armor to add to the equation until 1916.
Armor started out in a weird place on the battlefields of Europe and the Middle East. One of the methods that finally helped both sides unlock the Western Front stalemate in 1918 was achieving operational and tactical surprise while simultaneously amassing the firepower needed to achieve breakthrough and the reserves to maintain an advance once the front line was broken. This was an extraordinarily difficult thing to do! Since the Germans relied on artillery for their firepower, they solved the problem by developing extremely thorough means of maintaining operational security, and by improving their fire support and artillery preparation procedures to minimize the length of a bombardment while simultaneously maximizing its destructiveness. Tanks were the Allied solution. They could be massed quickly, without need for a lengthy artillery preparation, and they were at least somewhat mobile, albeit unreliable. Armor made General Mangin's counterattack at Soissons in July 1918 - the turn of the tide on the Western Front - possible. It was a strategic surprise, because OHL had convinced itself that the French military was incapable of further offensives, but it was also an operational surprise, because German higher commanders could not detect Entente preparations until the tanks were literally rolling into the German trenches.
Since armored attacks were largely conceived of as a way to eliminate the need for artillery preparation, it became difficult for some Allied leaders to conceive of them as working together
with artillery. Everybody understood that tanks and infantry needed to be closely coordinated in theory, although the breakdown of that rule in practice made for high casualties among Allied tankers. But few people grasped the notion of coordinating them with other arms, as well. Even the British and Commonwealth efforts to closely coordinate their fires in the fall of 1918 looked less like modern combined arms: the various elements of the army were being employed in the same place, but not necessarily
synergistically, if that makes any sense. (For what it's worth, there are some historians who argue that the BEF
did have a concept of synergistic combined arms. I disagree, but it's a reasonable argument.)
Between the wars, many militaries developed a better understanding of combined arms. (Some armies developed a
worse understanding; a few British officers with high profiles became convinced that tanks could fight on their own without any infantry at all, which was absurd on the face of it and led to considerable friction within the service with those officers who weren't so given to fantasism.) They also developed the most important tool for making it possible: the man-portable radio. Battlefield communications in the Great War were generally based on runners, flares, and signal flags, which made coordination almost impossible (and led to a frightening amount of fratricide from artillery units on both sides, even late in the war, as memorably related by Ernst Jünger in
Storm of Steel). The radio unlocked that particular problem and made it possible for forward infantry and armored units to call for support more or less instantly.
The Germans, however, were the first military to create formations that were capable of actually synergizing the various components of an army. The real genius of the early-war panzer formations was that they had enough infantry, artillery, pioneers, AT weapons, AA, recon light armor, and so on, and so forth, so that each panzer division, in conjunction with close air support delivered by the excellent system of
Luftwaffe liaisons, could operate as a single coherent combined-arms unit. The French Army also made efforts toward developing a unit that could execute a combined-arms mission - the "mechanized Light Division" (
Division Légère Mécanique, or DLM) - but there weren't enough DLMs and they were in the wrong place at the wrong time when the panzers came crashing through the Ardennes in 1940. Also hampering the French was that many French tanks were designed so that only commanders' vehicles got a crucial radio; German tanks allotted a radio to each one, which made coordination and organization on the move possible.
By comparison, the British Army still concentrated its tanks in extremely tank-heavy formations with few attachments of relevant things like "infantry", and sent them charging at enemy AT fronts as though they were the Light Brigade in the Crimean War, an unflattering description which has not needed modification with time. It took until the second half of the war before the British military started making combined-arms battle groups. Even then, coordination between arms was poor; there was a significant disconnect between artillery and everybody else, and another between infantry and armor, which led to a lot of unfortunate situations. The Royal Engineers and the Artillery were outstanding technicians, but failure to closely communicate with infantry commanders led to either a lot of dead Tommies or a lot of Tommies who couldn't get past the LD. Neither one of those is conducive to offensive success.
The US military took its cue for organizing its armored divisions from the Germans, with a decent amount of homegrown theory and experience. American armored divisions of the 1944 model were amply supplied with infantry and not just tanks (although they did have an impressive
number of tanks that American generals even managed to effectively command and control), were almost always fully motorized (unlike German panzer divisions, which were lucky if they could get halftracks to motorize even one of their infantry battalions), had better access to self-propelled artillery, and could draw on an even mightier air force than the early-war
Luftwaffe for backup. The "combat command" system that the Americans developed, of structuring armored divisions in semipermanent subunits that were explicitly designed to be
ad hoc independently operating combined-arms formations, was also wise; it drew a great deal from the German
Kampfgruppe method, the British battle group, and so on. To top it all off, the US even developed some tactical innovations that the panzers and
Luftwaffe had lacked, like Pete Quesada's concept of continuous fighter-bomber armored column cover that worked wonders in the fighting in France. The Americans needed two years to work out the bugs from their ideas about ground warfare, but once they finally did it the US armored division was probably the most fearsome such unit on Earth.
Soviet theorists came up with their own innovations in armored warfare. When making the first stabs at turning the ideas of "deep operations" developed by Svechin, Triandafillov, Tukhachevskii, and others into a real doctrine, Soviet officers came up with the concept of a mechanized corps. Like the British tank formations, however, mechanized corps were much too armor-heavy compared to infantry, and they were also probably too large to effectively command. Red Army officers were clearly unhappy with the concept based on combat experience in Spain, but they were unsure about how to best improve it, which along with the purges goes some way to explaining why the mechanized corps were disestablished and then suddenly reestablished in the years immediately before the Nazi invasion. During the desperate fighting of 1941, the naysayers' fears came true: the mechanized corps were ineffective on the battlefield and possessed little capacity to maneuver effectively. The mechanized corps were done away with once again during the fall of 1941 and the entire tank force was reorganized in units no larger than brigade strength. As the war ground on and Red Army commanders gained experience, they slowly rebuilt larger armored formations until six whole Tank Armies - the equivalent of a German panzer corps in firepower - existed from 1943 onward. A Tank Army, however, were more exploitation force than integrated combined-arms unit, at least in theory; in practice, they were usually reorganized to add enough infantry to make them effective.
One of the most useful Soviet combined-arms techniques from 1942 onward was the forward detachment. Armored officers in the Second World War were quite aware that reconnaissance units would have to fight to maintain an effective screen and gather intelligence, so they were equipped with vehicles designed for light armored warfare: the German
Achtrad and
Puma scout cars and the infamous Sd. Kfz. 222, the American M8 Greyhound, the British AEC and Staghound Armoured Cars, and so on. The Red Army went them one better. Soviet forward detachments weren't meant merely to fight for their information, but to actually maneuver tactically and conduct penetration attacks. They were used by both tank and rifle formations during the war, tailored specifically to the needs of the moment (deep penetration attacks by tank forces would need a different sort of forward detachment than defensive operations on the flanks by rifle forces), and served as the fundamental basis for Soviet combined-arms doctrine after 1945. Soviet development of the motorized rifle division's structure would not have been possible without the forward detachment concept first imagined in the 1930s and then tested and improved in wartime.
So, to answer the question:
Doctrinally, the Germans were not the only military that had ideas about combined arms in the 1930s. Soviet and French writers did, too, along with some Americans, and the Red Army and French military had gone to some efforts to put those ideas into practice. But in terms of force structure and inter-service cooperation, the
Wehrmacht was the military that was able to make those ideas
work well on the battlefield first. When Guderian's XIX Army Corps (mot.) fought its way across the Meuse River at Sedan in May 1940, it fought perhaps the first well-run combined arms battle in world history.
I'm sure dachs will correct me,
that really needs to stop being a reflexive thing to say on these forums
but all major countries were experimenting with combined arms since late in the Great War. It was just a matter of figuring out how to put it into practice and getting the equipment needed to carry out combined arms well. The Nazis initial plan for WWII was a quick thrust into Belgium so they could threaten the channel and then settle down into a war of attrition and hope the Allies would settle for peace before the German home front collapsed. The great emphasis the German military placed on combined arms was in part due to how they had been undergoing re-armament for longer than the Allies and in part because they knew they didn't have the industrial, financial, or manpower resources France or the UK could call on (and the less said about America the better) and put a lot of effort into figuring out how to perfect the Napoleonic maxim of concentrated force.
Looks about right to me.