Later in the war, Hitler did order the execution of commanders who abandoned fortresses. Some were actually carried out. But by then, the Germans were eating their own.
Hausser’s abandonment of Kharkov came with the full approval of Field Marshal von Manstein, who covered for him. Von Manstein is even now preparing his counter-stroke, “the Miracle of the Donetz” whereby he will temporarily recapture Kharkov and Belgorod, and restore the situation in the South. The thaw and exhaustion will prevent him from eliminating that pesky salient around Kursk, however.
Maybe he’ll get around to that later.
But Hitler will not forget that Hausser abandoned Kharkov, and because of that he will be passed over for promotion to the elite SS Panzer units. Hausser will eventually be stuck commanding 7th Army in Normandy, a non-SS unit, when it is destroyed in Operation Cobra.
The problem with FM Paulus, the commander of the Sixth Army at Stalingrad, was that really was intimidated by Hitler and a total Hitler loyalist. He knew from the outset he had to break out of the Soviet trap immediately. But Hitler ordered him to stay put. FM von Manstein urged him to break out and defy Hitler, but Paulus was too timid to defy Hitler and always obeyed Hitler no matter what, except at the very end, when on just about the last day of the battle, Hitler promoted him to field marshall with the expectation he would commit suicide. For the first time, Paulus refused Hitler and surrendered his army and went into Soviet captivity. While in captivity Paulus turned against Hitler completely and became part of a Soviet propaganda effort aimed at encouraging German troops to give up and surrender.