Slitherine

My cause for the day, Paratroops.
1. You purchase one of these guys.
2. You move him to airfield hex.
3. You embark on plane and take off.
4. Arrive at objective (usually two turn flight).
5. Hit the silk over drop zone.
6. Make your attack, if your not destroyed.
That's six long turns from purchase to attack. That is 1/4 of most battles!
I think if the transport has movement left, you should be able to drop on the third or fourth turn, depending on distance to drop zone.
Also, do fighters and bombers use fuel loitering over battlefield?

I hear you and find paratroop operations fairly nerve-wracking. However, if you buy them during the deployment phase and deploy in the air, that's two of your turns saved. Realistically they wouldn't fly more than 1 turn (I know there is nothing to stop them flying around forever in the game), then drop. Arnhem was supposed to be relieved by Horrocks' XXX Corps, the 101 and 82 by the Normandy landings, Crete was probably the only one (that I know of) where support was not (theoretically) close at hand. Anyway, what I'm saying is a 'normal' drop would take 3 turns (not 6).

I think planes use a certain amount of fuel just by loitering, but I'm not sure how much (or even if I'm right).

Yes as long its isn't in any hex airfield or adjacent one, the plane will consume the same has traveling to an adjacent one.
It won't last forever.

Paratroopers is sometimes the ONLY way to get a decisive victory on the hardest difficulty settings.
Many scenarios have room for up to 6 air transports, and as paratroops can be deployed already in their JU-52s, you can completely skip steps 1-3 and fly directly to a rear area enemy objective and siege it in a relatively short time.

Baku, for example.

Yes I used paratroopers in your Hylan Valley AI challange, they are tough little buggers. I like to gain air superiority by taking all the airfields also.