As I understand it, the military objective of capturing Stalingrad was to be able to cut off north-south river traffic on the Volga, and land traffic on the east bank of the river, using the city as a base for air and artillery strikes. In fact, the original plan for Fall Blau had the Germans going up to, and screening the city, without actually entering it and engaging in city fighting.
During the battle of Stalingrad, the Germans captured 90% of the city (but a decidedly smaller proportion of the west bank of the Volga). Nevertheless, the Germans held portions of the west bank both north and south of the city on which they could place artillery and air units to disrupt Volga River traffic. Per the Wikipedia article:
"After three months of slow advance, the Germans finally reached the river banks, capturing 90% of the ruined city and splitting the remaining Soviet forces into two narrow pockets. Ice floes on the Volga now prevented boats and tugs from supplying the Soviet defenders."
Was there any time prior to the encirclement that the Germans' military objectives would have been substantially fulfilled by consolidating their holdings and "ring fencing" the remaining portion of the city while they wen about their business (like setting up a defense)? Or did they need the last 10% of the city for military reasons?
Please note that I am NOT asking about political considerations such as the prestige value of taking or holding the city.