I would assume paratroops can get there faster since they are flown in and don't walk or drive in. I guess you do need to explain to me why a mech corps with 90,000 men and assorted vehicles does not immediately convert a hex in game like a para brigade, with a couple thousand men. I don't see how they can control the space more effectively than a unit 50 times larger does. I have to wonder if that was the intent of the devs.
It's not a matter of 'control space more effectively', but it is a matter of movement costs.
XXX Corps rolling over roads and bridges controlled by paras doesn't have the same considerations as they would moving through enemy controlled territory. That 'cost' is borne by the airborne (in lost men, readiness, and airframes).
Consider, in games terms, the motorized cost of Operation Garden without Operation Market:
Minor River hexside (No EZOC) +2
Minor River hexside (EZOC) +6
Major River hexside (No EZOC) +4
Major River hexside (EZOC) +18
Several rivers, 10 to 20 miles apart, that in game terms XXX Corps could never traverse in one week unless friendly controlled. Immediate conversion can represent factors like seizing bridges before they are blown, reduced need for scouting and recon, and similar factors that explain the higher cost of moving into enemy territory. In point of fact, the operation failed where the paras failed to seize bridges.