Went into this one in detail on another form several years ago. At the level of the corps the US Army was heavily armored. The armored cavalry squadrons and groups, the independant tank battalions & TD battalions all made the US corps of two or three infantry divisions well armored. The British corps more so as they had a slightly higher ratio of tank to infantry battalions in a corps of two or three infantry divisions. In both US & Brit corps the ratio goes even higher where a armored division replaces a infantry div in one of these corps.
At the Army level the ratio of armor to infantry and artillery battalions is just as pronounced.
All this is aggravated by the chronic understrength of the German tank & assualt gun or TD formations. When you compare on a individual tank to rifleman basis after 1942 the German Panzer Divisions or Corps hardly qualify as armored formations compared to a US, Brit, or Red Army equivalent.
The US did test a "Armored" Corps in 1941-42 as well as a mechanized corps. The organizations proposed for both proved awkward and actually less capable than the standard crops organization already proven. The corps Patton commanded for the Torch Operation in November 1942 was labeled a "Armored" Corps... but this was only a name as the features of the proposed armored corps had been discarded after the last trials in 1942.
... My suggestion is 2 Corps each with one 'heavy' AD, one 'light' AD and an ID with extra half tracks and trucks and another AD as the Army 'reserve' formation. This would be the bare bones of the Armoured Army, the Army AD could be added to to make it a theird Corps if need be.
This is not far from the Armored type corps tested to 1942. In 1941 manuver General Krueger defeated sucha formation by aggresively concentrating his armys AT guns and supporting them with minefields and artillery. The tanks found they lacked enough infantry/artillery support to clear the AT guns or enough engineers to clear the minefields & road blocks, and replace demolished bridges. Think of the PaK fronts Rommel & others created in Africa or Russia to defeat Brit and Red Army tank attacks. The second serious probl;em the US Army found was the dense concentration of tanks created massive traffic jambs as the roads clogged with their endless supply columns. When the trucks tried to move forward they became vulnerable to deliver they were vulnerable to enemy fire. if the tanks withdrew to the trucks it aggravated the traffic problem. Thinning out the front was not a solution as the remaining tanks were inferior to infantry and artillery for covering the intervals between assualt groups. All this was similar to Brit, Red Army, or German experience. As the war progressed everyone reorganized their mobile or mechanized formations in a search for a balanced combined arms organization.
In that other discussion I noticed a assumption that a formation of predominatly tank battalions was a better 'armored' force than those similar to the US and British corps and armys. However it appears that a tank heavy organzation of division or corps size is less effective than one with a larger portion of infantry and artillery battalions. While a 1-1-1 ratio of tank/infantry/artillery battalions seems to work at the division level the need for tank battalions falls off at the corps & army levels with a higher portion of infantry & artillery battalions needed. This seems to be reflected in the mix the Red Army grouped for mechanized combined arms operations above the division level.
The problem of the German panzer corps or panzer army is that after 1941 the armored divisions were increasingly paired with unmotorized infantry divisions. Frequently the "panzer armys" had the majority of their artillery still horse drawn and the grenadier battalions riding rail cars or walking. There were never enough automotive trucks available to the German army to properly motorize enough infantry divisions to properly pair off with the armored div for forming true armored corps or armys. The largest single armored formation, 'Panzer Group Kliest', had only three motor rifle divisions supporting seven armored divisions. Had their enemy been better prepared the lack of artillery and infantry would have been a problem, as it was later when smaller tank heavy German panzer groups attacked capable enemy defenses.