but that was an attack on a fully equipped enemy which had had 4 years to prepare against invasion
But the logistics of transporting an assault force and then supplying them was essentially the same but on a smaller scale. The Germans had nothing in readiness and were only ever going to be able to cobble together the transport. Yes the Luftwaffe had a lot of kit but they were structured to achieve a breakthrough at the Schwerpunkt on a frontline in a land battle. Their paratroopers were decimated at Crete where the Commonwealth Forces were in a similar situation to the Home Defense of England. If Freyberg had held onto Maleme airfield then Crete would not have fallen. So extrapolate that relatively small battle to an invasion of England without air superiority and command of the sea.