Again the with the main strength of the luftwaffe we are talking thousands of war planes in theater instead of the few hundred historically. German air transport could of also been brought to bear. Many panzer divisions were resupplied by air in the Russian campaign when they outran the normal logistical support. And in the winter of 41-42 pockets of surrounded German divisions in russia were supplied for months by air. The Germans were able to reinforce and supply 250,000 men in north Africa in Tunisia in the winter of 42-43, almost entirely by air, even after the losses in air transport at Stalingrad.
So after the conquest of Greece and Crete there was an opportunity for the Germans. British strength in Egypt was depleted by redeploying men to Greece and the losses there. If Crete and Sicily were made major luftwaffe air bases along with others established along the Libyan coast any British ships attacking convoys from Italy are in great danger. Further Libyan air bases with bombers can now hit Alexandria naval base and the Suez canal. Air transport with Condor transport planes augment the convoys and keep Libyan air bases supplied. Quick transfer of panzer divisions to north Africa followed by a push through Egypt. With significant air support convoys can get through to Libyan ports closer to Egypt like Tobruck and Benghazi (!!). Uboats deployed against the British own highly extended supply chain around Africa and the bottleneck at Gibraltar threaten to turn the tables on the British and choke them out.
And that's without considering a more concentrated diplomatic campaign directed against Turkey and Spain to either join the axis outright, allow German divisions to transport through their territory to attack Gibraltar and the middle East, or face conquest by Germany thus allowing attacks on Gibraltar and the middle East.