Look here, the logistics, especially in the first vital weeks of the advance, are already WITHIN range, especially of attack and Jabo missions. The problems of hauling goods kicked in when the fields were far inside the front, and had a bad road connection. But from border based airfields at first, there is no way you can convince me that fewer aircraft (and pilots) were a better choice.
Nor that a much higher amount of reserves would have been bad.
As for the bad road connection, yes, I know. But just not at all times. And then there is no way that a better airlift would not have helped. It was not just about hauling tonnage and fuel, it was vital spares etc etc.
BTW, a serious transport loss in the med occured before Barbarossa, i.e. Crete.
The later transport losses were mostly in Tunisia at the time of Stalingrad, but that's not Barbarossa.
IMHO the Luftwaffe did play a major part. They were vital in the anti-tank role and they were practically the key to making the blitz so fast. And they came close to wiping out the Red airforce.
For victory, IMHO, the Axis needed more of everything, including time. But to repeat, I think just 2000 aircraft for that big an operation was to small, - it just happened to be what they could muster.