Well, as I noted up far the thread, the Germans simply didn't play from the same doctrinal rulebook...one that was simply not as far attenuated as -There wasn't much wrong with the ordnance itself, apart from being mounted in a tank turret with limited space for recoil mechanisms. The use of Howitzers as a close support weapon for a tank force is fine. One of the problems with the SP Birch gun was that it was a gun and could not be used to seek out an enemy in dead ground. Nor was the solution very different from the low velocity 75mm gun in the Pz IV. The Germans used the combination of howitzer equipped PzIV and cannon equipped lighter tanks to great tactical effect in 1939-41. But the Germans grouped their howitzer equipped tanks into Heavy platoons in the medium companies, and gave them a sensible role. Furthermore, the Panzer units were part of a panzer Division of all arms including anti tank, AA and field artillery giving German commanders a far wider range of tools to tackle tactical problems.
...all that "successful" experimenting and theory testing in the late '20s and early '30s in the UK having "proved" the theories. The two experiences developed from different starting points, however - the Germans' from having to make the best of what they'd have...the 1920s British armoured warfare theorists starting from the premise of what they'd like to see armoured and combined arms units doing! Of course the two results would be different.The problems were in the thinking of the extremist armoured corps enthusiasts who dominated after they fell out with the Gunners and Lindsey, Broad and Pile left for other appointments. There obsession with the idea of the role of tanks in the pursuit, the essence of Blitzkrieg blinded them to the need for tanks formations to be able to operate in other phases of war where a combination of arms might be needed.
However...
I'm not sure this is the case. There might have been "little though given" by the Royal Armoured Corps...for some reason a lot more "rivet counter" study has gone into the cruiser tanks...the vehicles themselves and their use - but nowhere near as much into who/when/where the idea of dedicated "I" tanks came from for the initial assault/breakthrough battles ...but that's one for a separate thread....There obsession with the idea of the role of tanks in the pursuit, the essence of Blitzkrieg blinded them to the need for tanks formations to be able to operate in other phases of war where a combination of arms might be needed.
There was little thought given to how tanks would work with other arms or training in combining them. As has been pointed out, no great priority had been given to providing HE ammunition. As late as 1941/2 the War Office released a film show casing how tanks were used in battle, showing an armoured brigade ambushing a German tank force. Apart for an RAF aircraft which spotted the location of the enemy column no other arms were involved.