Historically we saw the Germans steamrolling over the French and British in 1940 with their massed Panzer divisions across Belgium while the Allies spread their tanks largely across the frontlines.
A generalization. The French had numerous motorized/armoured/hybrid cavalry units such as the three
Division Légère Mécanique, the five
Division de Cavalerie Légère, and the three
Division Cuirassée.
This number compares somewhat favourably to the ten Panzer Divisions which the Germans were able to field in 1940. Also, the counterattack at Arras by British 1st Army Tank Brigade inflicted a sharp local reverse on 5th, 7th Panzer and SS-TK. The issue was not that the Germans were the only ones to field large armoured/motorized formations: it was that they had more experience and training in the techniques of a modern all-arms battle, and were not so handicapped by inter-branch rivalry as the more conservative Allies at the time, hampered as they were by the confirmation of old methods that victory in WWI had given them. Similarly, the bulk of Allied mobile formations were trapped in an impossible strategic dilemma: expecting a repeat of 1914, they rushed north towards the line of the River Dyle, only to be wrong-footed with their backs to the sea by the main attack coming in with complete strategic surprise behind them through the Ardennes. No one can fight effectively without supplies and secure rear communications. This is why you didn't see really large tank vs tank battles too much in the 1940 campaign (probably greatly to the German's benefit, since their fewer and lighter tanks might well have come off the worse in such an exchange): the Allied armoured units were rushed in to the wrong position to await an illusory main thrust, and then got swept up in the general collapse without much chance to show what they might have done.
and find what Germans called Schuwërpunt or breaking point while the rest of the army held the front
You mean "Schwerpunkt", which literally translates as "heavy point" but might be better understood as "the point of maximum effort". It referred not to the technique of assault, breakthrough, and exploitation itself, but rather the command philosophy that it is better to suddenly strike a weak spot with concentrated fighting power on a narrow front, than to grind up your manpower and momentum pushing weakly along the whole line. Should also state that although the vast preponderance of the supporting fires, Corps and Army artillery, close air support, etc would go in to the Schwerpunkt attack, units in the line to the left and right of this would generally not be idle: they would put in diversionary attacks, just strong enough to keep the enemy from shifting forces away from them to fight against the Schwerpunkt attack. This depended on infantry with a high degree of offensive drive and initiative, which the Germans certainly had in abundance in the early war years.
The Germans concetrated their tanks in panzerdivisions, which in 1939 had one panzerregiment and 2 motorised infantry regiments.
Actually you've got it in reverse
The 1939-1940 Panzer Division organization had two Panzer Regiments, and a Schützen-Brigade composed of a regiment of motorized infantry and a battalion of motorcycle riflemen. This alongside an artillery regiment, and the normal assortment of supply, signals, medical, engineer, recce, antitank battalions. The ratio was reversed with the 1941 reorganization, to one Panzer Rgt and two Panzergrenadier, and stayed mostly unchanged for the rest of the war. More organic infantry made the tanks more self sufficient in operations, and also reflected the inability of German industry to provide enough vehicles to fill out the growing number of divisions of the rapidly expanding Panzerwaffe.
The americans in 1943-1945 had at least one tank battalion in each infantry division. Then they had armoured divisions.
Should specify that these tank battalions were not organic to the infantry division structure, but became a de facto permanent attachment to most divisions assigned to the Med and NWE theatres, similar to how the Chemical Mortar Battalions were doled out. America could afford this because, well, America.
All US and UK infantry divisions except for, special units, were motorised.
US infantry divisions were not in fact formally motorized, ie, having their own trucks as part of their permanent organization. What they did have was access to the absolutely immense fleet of general service vehicles that accompanied the US Army everywhere it went, and split their time between supply and troop movement tasks as ordered by higher command. In cases where speed was necessary, entire divisions could rapidly be put on wheels in this way, but it should be understood this was temporary, and most infantry GIs did an amount of marching that would not have shamed their ancestors in the 1860s.
Also, only the BEF in 1940 was fully motorized, as it represented the best of Britain's small, professional prewar army. That ambitious target rapidly fell apart after the collapse in France, and from that point only the infantry brigades in armoured divisions, and the motor battalions in armoured brigades, had full motorization. Everyone else marched.
This and other things meant that the German infantry divisions in general had less offensive power(and it would get worse as the war progressed).
So if we take all the things in account:
1. The infantry of the panzerdivisions were often the only motorised infantry units = the panzer divisions were the only "fast divisions"
2. As the war progressed the panzer division more and more become the only divisions with offensive capabilities
There is a widespread belief that only tanks had offensive power. However, considerable numbers of highly successful attacks were carried out by infantry with no tank support at all. The key difference infantry of the 1940s had compared to their fathers in WWI was that the infantry heavy weapons, the machine guns, mortars, and other equipment that provides the bulk of their fighting power, were now
portable. All that stuff existed in 1918, but was much less mobile and therefore there was a huge firepower gap between defenders, secure in their entrenchments with their full arsenal, vs attackers who had to struggle out in to no man's land with rifles, bayonets, grenades, and not too much else. The first inklings of really portable crew-served weapons only started to come out at the end of that war.
The key difference in infantry vs armoured offensive potential is not so much smashing power, which both could have if led and supported correctly, but operational ability to
exploit that breakthrough. Infantry could and did make a hole in the line, but was too slow to turn local tactical victory in to a real strategic success, by striking deep in to the enemy rear to cut supply and lines of retreat, etc.
Well that's a lot of Jamor nerding out. To answer the OP's original question, yes, multi-division all armoured/motorized formations are historically accurate. Germans and Soviets did them all the time.
(Edited caveat: of course, because nothing about WWII is ever simple, some notionally "Armoured" armies would, due to the natural transfer of units and and out, gradually lose their armoured character. Usually they would retain the name, probably for purposes of morale. Look at poor, forlorn 2nd Panzer Army in 1942, stripped of all but two of its Panzer Divisions to support offensives elsewhere:
http://niehorster.org/011_germany/42-oob/42-06-28_blau/mitte/army_pz2.html )
