Let’s say that Hitler orders 6th Army to surrender after it is encircled.
That would open up the only major supply-route (railway via Stalingrad) in the southern sector of the eastern front.
Soviet armies (lot of them were trying to move forward but could not because of the lack of supplies) would get ammo, fuel, etc… enabling them to roll forward, before German could setup the new front. Soviet armies would take Ukraine, outflank the German Army Group center, cut the supply lines of German forces located in Caucasus. WWII would be over, pretty much immediately?
Forcing the 6th Army to continue fighting was essential (only sensible solution):
- it tied up a lot of soviet armies
- it left rest of the southern sector soviet armies without supplies
- it gave Germans time to setup a new frontline
- it bought enough time to evacuate German forces from Caucasus
_