Would have been a complete disaster making market garden look good in comparison.
Remember you have no effective command and control elements at this point which you need for a division. At D-day where radios were available 101st and 82nd had no contact with 50% of their forces and a few german battalions in a theater very sparesly populated by the enemy inflicted very severe losses on said unorganized forces. Here you have a very densly populated theater with no opportunity for such a force to rally and get organized.
If anything such a proposal will probably discredit the paratrooper idea and make people give up on the entire idea before it has a chance to mature.
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I don't disagree about the lack of command and control, or the fact that it had a high probability of failure. The plan was to drop them 4 miles from the front, just behind the German artillery formations (this would have been in full view of the allies along the front, specially thru observation balloons) which will then initiate their offensive along the front. The idea was not to attack from the rear but rather to dig in and prevent the retreat and reorganization of german forces. Casualties would have been horrendous, but a gain of four miles (or even half that with the loss the entire group of paratroopers) in an offensive would be seen as an spectacular success in an war where an offensive was deemed successful if it moved the front 100 yards. Considering that the HP400 was estimated to carry 8 people (paratroopers) at most they would have been able to drop 800 soldiers in the operation, not an entire division at most a bn (but i digress). As sad as it was, the loss of an entire bn in an "successful" offensive was considered acceptable at the time (entire brigades were lost to gain a lot less).
Another reason that increases their probability of success, would have been that this was the first use of paratroopers during a war, with effect similar to those caused by the first tank offensive in ww1 and the first airborne use in WW2. The fact that there was no heavy AA defense behind the front and many others factors. In market Garden the drops were successful and concentrated with most of the units hitting the correct drop zones. They were not expected to maneuver out of the DZ and seize objectives, the plan was to dig in on the drop zone and prevent reinforcement from moving forward and the enemy from retreating.
However, my post had nothing to do with whether the operation had succeeded or not, it had to do with answering the OP question about putting paratroopers under the Air Force. So, I Stand by the answer that if the operation had been carried out and if the operation had been successful (two big If's but not ASB) there is a justification for the air service to use them as the reason for service independence thus keeping the paratroopers under the Air Force in US service