ljdaw, I think you phrase your opinion a bit roughly and it leads to a lot of misunderstandings.
Indeed, a panzer division was very much dependent on its "additional units", like recon sdkfz-s, signal equipment and units, the motorized and mechanized infantry regiments; and the lack of these could lead to abysmal performance, like in the case of the Battle of Arracourt, where neither the quality nor the quantity of the German armour didn't matter. Without recon and signal units, the tanks arrived piecemal in a series of disjointed assaults.
However, you are going into the extremes when you say the number of tanks was irrelevant and that a panzer division cannot move fast enough. Of course there were adverse effects like road quality, weather and such, but in general a panzer division took 95km of road without intervals between the units, and so approximately 100km in reality.
The march speed of tanks was 12kmph, but the infantry of the panzer divisions - a motorized infantry regiment on lorries and a mechanized infantry regiment on half-tracks - could march with 22kmph and 16kmph, respectively, so your statement when you said that
3 A tank batallion is a PART of a division and if it is advancing 100 km in one day, this does not mean that the whole division is advancing 100 km .
is not really true, because in an adequately motorized panzer division, it was actually the tanks that moved the slowest, and produced the most mechanical breakdowns; so if the panzer regiment
of a panzer division could in reality move 100km in one day, then the rest of the division could follow.
Also, if you change one mechanized infantry regiment to a panzer regiment, then you change a 12,020m march section for a 19,500m march section, so the difference is not that big as you suggest here:
If a column of 100 tanks need 10 km of road, a column of 10 tanks will need less km of road .
So if you double the number of panzers in a panzer division, and half that of the motorized infantry, the division will take +7.5% of road and will travel with the same speed, theoretically. If you don't touch the motorized infantry units, but double the panzers, the division will take approximately +19.5% of road.
Back to the number of tanks.
Again, you are confusing campaign or battle results with effectiveness. If the task that was given to a panzer division was impossible to do, then it doesn't matter how effective was it compared to a battle where the task was possible to do. It's nonsense. It's not realistic to say that the Germans lost the Battle of Kursk, so their panzer divisions in mid-summer 1943 were worse than those in 1940, when they've won the Battle of France. The two were very much different operations.
So first we need to address the deployment, the overall situation, and then we can conclude which unit composition was the best suited for the task.
I agree in principle that the panzer divisions for Barbarossa were reorganized in a better fashion = more suited for the task at hand (with one panzer regiment) than the ones in 1940. Mostly because the plans of Barbarossa contained multiple encirclement operations, for which the Germans needed a lot of motorized or mechanized infantry.
But in 1940, the panzer divisions were organized in a good fashion, too - because then the concentration of armour mattered the most in their plan, and additional infantry units were not as much important as the unified command of large panzer formations.
Aside from that, Germany could not profit from much more tanks in the Fall Gelb; that plan was not built upon that. (It was problematic to cross the Ardennes and the Maas with that much units anyway.) Also, the campaign was over in a few weeks.
Unlike the campaign in the Soviet Union, where the campaign(s) lasted for years, and so maintenance and supply became insanely important. Until the summer of 1942, the collapse of the centralized maintenance system was not addressed sufficiently, and even later on, it wasn't addressed adequately. Repairing tanks became ever more difficult, especially when the long retreat began. So operational readiness rates - thus combat effectiveness - could be increased with increased amount of production; let it be the production of new vehicles, spare parts or whatever.
"Everything remained theory and hypothesis. On paper, in his plans, in his head, he juggled with Geschwaders and Divisions, while in reality there were really only makeshift squadrons at his disposal."