So what would the altered effects be if Paulus had linked up with the 4th Panzer Army? What if Hitler had allowed Paulus to retreat? The history has been discussed, but not the potential outcomes if something was changed.
Paulus didn't chicken out. He was loyal to Hitler and thus waited permission. I think he learnt that personal initiative can lead to some stupid acts of heroism.
Paulus refused to act when he had a chance. He was more affraid of Hitler than of the Russians. Part of the problem was that Paulus had never held a combat command. He was a staff officer and not suited to making decisions that he would be resonsible for.