Quite right to say that , actually you show us another mistake - shifting the major power of the offensive in a town ( which even if taken won’t resolve much of the problem as the oil fields will be free ) - a battle which was more for prestige and showing power to the enemy rather than a huge strategic target . Even if we imagine that the german forces were in Stalingrad and fully occupied it ( of course by the end of the fight it would be hard to say that this was city anymore rather a ground filled with ruins ) the oil in Baku will be still intact and working and i suspect the soviets will be still using it mainly with transport trough the Kaspian sea maybe instad of transit trough Stalingrad
The core problems of Stalingrad lay in the Fall Blau directive. The initial march to Stalingrad was viewed as being a rather simple scenario by the Germans. In fact, at one point, Hitler was so sure the city would be taken without a fight that he redirected mobile units down to the South via Rostov to support the drive to Baku (which caused huge traffic jam problems). The Russians were initially ready to give up the city (they didn’t see it as that big a deal at first) but decided to reinforce once the Germans began tripping over themselves in the advance to it.
The winter didn’t actually play a big part in Stalingrad. The Germans had learned their lesson in 1941 and were prepared for it this time.
Hitler was the biggest problem the Wehmacht faced. Going back to Blau, the plan was ridiculous to start with. The drive into the Caucasus was envisaged as an easier “part two” of the campaign. There would be little need of flank security (and there were a LOT of open flanks during the drive south but the fact that the main battlefield was in the city kept either side from reinforcing enough to take advantage of it) because the Russian would be defeated beforehand. Hitler was convinced the Russians had “shot their load” in the Kharkov offensive (which failed miserably) and was further convinced of that when Stalin and Zhukov ordered the units in the South to simply fall back instead of contest the German attack after Blau began. The Germans weren’t bagging large numbers of Soviets so they didn’t think there were large numbers left to “bag”. Also, the Russians didn’t reinforce right away because they still thought the main blow would come against Moscow. They believed that the attack in the South was either a feint or the Germans would advance on Moscow from the Voronezh area.
Once the Germans were in Stalingrad, they were stuck. They did almost take the entire city but it was a phyrric victory of sorts and a complete waste of resources. But the hedgehog that formed there after the Soviets encircled the city kept the Soviet armies from advancing to cut off the German troops in the Caucasus.
Overall, the entire concept of Fall Blau was self-defeating from the start. It did not have the potential to cripple the Russian army (as has been pointed out, the Russians could have rerouted the oil they produced) nor would the oil fields aid the German army (at least in the short run). It stretched the Germans beyond their supply capacity and forced them to rely on poorly equipped Romanian and Italian armies to cover their flanks. It was a FUBAR from the start! Of course, hindsight is 20/20…