At least one would have been available and pressumably in better shap than units in Japan. Was it really so urgent to be ready for World War 3 breaking out at the South Pole while US troops were getting smacked around in an actual war zone. And how quickly could it have been available?
The 11th Airborne division was deployed to the Korean War
There were 2 para-jumps made by the US during the Korean War. Operation Tomahawk was the second para-jump and the more well known drop and the first one was the drop in support of landings at Inchon by a much smaller force.
This was the reason why the 82nd Airborne Division was not used in Korea
US Army, Europe (USAREUR) - 42,000 men
1st Infantry Division
2nd Armored Cavalry Regiment
6th Armored Cavalry Regiment
14th Armored Cavalry Regiment
7732nd Field Artillery Group (attached to armored cavalry regiments)
70th Field Artillery Battalion (105mm Howitzer)
74th Field Artillery Battalion (105mm Howitzer)
517th Field Artillery Battalion (105mm Howitzer)
519th Field Artillery Battalion (155mm Howitzer)
54th Engineer Combat Battalion (attached to armored cavalry regiments)
5th Engineer Combat Battalion
5th Antiaircraft Artillery Group
5th Antiaircraft Artillery Automatic Weapons Battalion
67th Antiaircraft Artillery Gun Battalion
2nd Constabulary Brigade
15th Constabulary Squadron
24th Constabulary Squadron
US Forces, Berlin (part of USAREUR)
7782nd Special Troops Battalion (Berlin Occupation Zone HQ)
3rd Battalion, 16th Infantry Regiment, 1st Infantry Division
16th Constabulary Squadron
US Forces, Austria (USFA) - 9,000 men
350th Infantry Regiment – 3 battalions
4th Reconnaissance Battalion
510th Field Artillery Battalion (105mm Howitzer)
77th Field Artillery Battery (155mm Howitzer)
70th Engineer Combat Battalion
Trieste, United States Troops (TRUST) - 5,000 men
7100th Headquarters, Allied Military Government Detachment
351st Infantry Regimental Combat Team
351st Infantry Regiment – 3 battalions
60th Engineer Combat Company
88th Reconnaissance Company
By 5 September 1950, the 82nd Airborne Division, 188th Airborne Regiment Combat Team (11th Airborne Division), and the newly formed 3rd Armored Cavalry Regiment are the only forces left in the General Reserve in the United States to reinforce NATO. Every other unit in the General Reserve had either been sent to Korea or had been gutted to provide units or individual replacements for 8th Army and 10th Corps. The National Guard, Army Organized Reserve, and the Marine Reserve units that have been activated will not be ready for deployment until March to April 1951.