While this seems a good mechanic to many, it complicates the game too much, your troops don't need transport, there's paratroopers and ballistic/aerial units are turned into transport trucks, and units taken over sea turn into transport ships, you already have what your wanting, but its more subtle.

My question would be;

What massive movement of troops via air transport would adding such a feature aim to represent?

I am unaware of any mass troop movements during WWII conducted using air transports. Paratroopers, mechanized units, tranport ships and the wearing out of boot soles by walking are all well represented.

First such troop movement that comes to mind would be Dessert Storm where USA used civillian ailiners to fly military personnel by the thousands to Saudi Arabia prior to start of that war. Not sure if it had been done on such a scale previously.

Well Vietnam also saw a pretty big commitment of US troops, and I'm pretty sure they didn't sail there.

But indeed, in WW2 almost all large-scale long-distance troop transports were carried out by ship or train.