A "support tank" is not obligatory an "infantry support tank". So, there is no contradiction on my side.
Guderian wanted tanks for large scale operations and not infantry support tanks. Fighting together with infantry is not the same. I think you don't want to understand that there is a difference.
An infantry support tank is constructed based on the requirements of the infantry. It was able to operate with infantry but was not suitable for large scale operations due to its technical conception. The caliber or the barrel lenght of the armament is not automaticaly an indicator. There were infantry support tanks which had only machine gun armament (Matilda I, Panzer I F).
All German pre war tanks (Panzer I - IV) were constructed for large scale operations. They had only thin armor (not very suitable for infantry support) and good mobility (around 40 km/h). Theses are technical and conceptional differences to infantry support tanks.
The choice of a gun with short barrel was not automatically based on the requirement to support infantry. At the beginning of tank construction in Germany, theorisers thought that a too long barrel could cause difficulties during driving in the battle area because of the barrel overhang. So, generally short barrels were chosen.
Additionally, I have never heard that Panzer IV's (L/43 and 48), Panthers and Tigers had any difficulties with their high explosive shels due to their much higher muzzle velocity.
You wrote: "...breakthrough" to be achieved by the infantry, supported by the IV, then exploited by the III supported by all other elements."
It dependet on the enemy, which units should be involved for a breakthrough. You should also have in mind, that panzer types were mixed in German armoured units. For example, a leichte Panzerkompanie a (1.3.1939) had Panzer I/II, Panzer III and Panzer IV. Even some German units spread their Panzer IV's over all companies. And for sure, the Panzer IV had its tasks after the breakthrough was achieved. Therefor, it was constructed for large scale operations.
All I want is, that it should be understand, that a tank which (sometimes) supports (or better: operates together with) infantry is not the same as an infantry support tank because of the main conceptional and technical differences. Therefore, it in not correct to designate the Panzer IV as an infantry support tank.