If Marines are part of the Navy, why does this not apply to paratroopers with the Air Force? After all, Marines were usually transported to their campaign / theatre by Navy ships and Paratroopers by Air assets. From memory, the Luftwaffe had the fallschirmjaeger, but I can't think of another Air Force that incorporated paratroopers into their organisational structure.
What changes after 1945 would need to take place within Western militaries for this to occur?