Ignoring the fact that Germany had no spare room for this increased output of trucks for military (what isn't built so they can be?) nor could it take them from civilian sector without causing serious disruption in moving of goods (as happened with railroad) this opens another problem. Logistics. Even in late July 1941 Germany had difficulties supplying their forces to proper levels, forcing pauses till supplies could be brough forward to sustain further advances (this became even more problematic during 1942 offensive but I digress). With additional numbers of trucks they have to be supplied with fuel and spares. While trucks allow goods to be moved further faster they require goods themselves (burning fuel to transport fuel, stressing trucks to move spares....) which in turn increases logistical strains even further. And that's assuming Germany has enough fuel to supply this expanded fleet.
Germany could concentrate supplies for one sector, likely AGC, depriving rest, forcing those on defensive. This in turn exposes their flanks, as happened in 1942.