I'm not sure that Paulus' ability to stand up to Hitler (or not) is relevant in this context. Standing up to Hitler became relevant when 6th Army was cut off, i.e. the order to stand fast and not break out to link with Winter Storm. The query is whether the Battle should take place in the city at all, but rather in open country. This possibility only exists in the opening stages, August, September and (maybe) October.
It is true that Hitler was determined to take Stalingrad and Stalin was determined to hold it. But that merely implies it does not matter which general commanded 6th Army. No German general would defy a Fuhrerbegleit when the Army was doing well (this is a feature often overlooked by groupies of the German General Staff - they only tended to stand up to AH when things were going badly.)
And in late August, on the outskirts of Stalingrad, Paulus and the rest of the German Army would have had every reason to suppose things were going well. But having failed to trap 62nd & 64th Amies in open country, they were then committed to attacking the city.
Now it could be argued the Ostheer could have tried a very mobile attack, like at Kiev or Minsk, a big encirclement causing a breakout or surrender. If so, Paulus' fault in attacking the city would have been overconfidence - he thought he could deal with the Russian rabble. But there were several factors against a big encirclement battle:-
(a) The difficulties of operating across the Volga with Stalingrad still in Russian hands.
(b) It would have been mid-September for such an attack to be organised, which would have given only one month (maybe) for it to succeed - in fact rain, succeeded quickly by snow, arrived in mid-October.
(c) Forces would have to be retained at Stalingrad, and with the Forces sent to the Caucasus, there would not be enough vehicles and troops.
There is also the fact that the Stavka people (Zhukov and Vasilevsky) had already started planning Uranus in September, and by October there was already a Red Army reserve of 12 infantry divisions and 5 armoured held beyond the Volga, earmarked for this offensive. This is in addition to such units as 13th Guards Div., which were fed into Stalingrad from time to time, just to keep the pot boiling.