I'll start by saying that paratroopers were not my idea, although I notice you used several of my suggestions about making them work 
I see paratroopers primary goal as securing an airfield in order for planes to penetrate deep behind enemy lines. Being able to smash the enemy supply lines and units that are still in transit to the front is one of the most effective ways to blunt their ability to react. Very few players have their units grouped with anti air or under the cover of interceptors behind the line. Of course this would only be safe to do when the enemy has gone to bed, as you would need to capture the province, repair the airfield for a few hours, and then pick off targets of opportunity.
So with that being my intended use of the paratrooper to capture an airfield and hold it against rebellion, the long cooldown periods work well.
Along the same theme as capturing an airbase, capturing a coastal province and building a naval base will accelerate disembarking significantly. Those 2 hours that could be saved can mean the difference between getting caught and getting safely ashore. The 4.5 hours of disembarking while hoping the enemy is not noticing causes a lot of anxiety.
An alternate use is for distraction, to cause the enemy to have to leave the front line and recapture provinces. This will weaken and disorganize the front line, hopefully creating an opening or at least a weak spot.
In all of these cases, I want to use paratroopers to seize and hold a province, so the long wait does not matter. I would leave the paratrooper there in that province for 24 hours or so anyway, at least until morale stabilizes and the area is secure. Why capture a province and then leave it behind to revolt or get recaptured by any single unit?
Now if the paratroopers are used against me, having them holding the province that they captured is obviously good as it makes them an "easy" target, and I can maneuver forces to recapture the province. However it does seem to be a bit like "shooting fish in a barrel" as there is no sport in hunting down the glued in place paratroopers. If the time that they are fixed in place is lower, part of the excitement is in guessing what the enemy is doing or has done. There might be a better province that is just out of range of the paratroop. I can relax with the knowledge that this province is safe from the air, but if the paratroop can land and roam free overnight it will be frustrating to defend against.
So I like the original cooldown times:
lvl1: 24h
lvl2: 18h
lvl3: 12h
lvl4: 6h
As they fit my anticipated use, and I can deal with having them used against me without completely unbalancing the game.
All this is entirely theoretical as I have not had time to actually try out these strategies yet.