All histories of the Stalingrad battle emphasise the heroic defence of the west bank of the Volga by the Red Army in 1942. It implies that if the German 6th Army had just managed to oust the last desperate defenders then by controlling the west bank they would have controlled the city and been able to declare some kind of victory at Stalingrad and change the course of the war.
No doubt the Russians holding on were fighting incredibly bravely. And presumably their prolonged defence of the west bank bogged the 6th Army down in a war of attrition which damaged the Germans' cause.
But what if anything would have changed if the Germans had taken the whole of the west bank? Other than a small morale boost?
They would still have only held "half" the city (my knowledge of the geography of Stalingrad is hazy but most cities which straddle a river have a substantial portion on either side). They would still have had over-extended supply lines and been exhausted and under constant attack from the opposite bank.
Most importantly Operation Uranus would surely have gone ahead in just the same way with the same final outcome.
So did it matter that the Red Army clung on to that small part of the city and, if not, why is such a big deal made of it?