If I could attempt to summarize in a few bullets what seems to have occurred, (Death by Powerpoint!), I see it like this;
Nobody in their right mind (at least in modern warfare) attacks a major city directly, especially when it can be reinforced and resupplied from outside the city. A modern, mechanized army loses all advantages when it attempts to attack a huge pile of ruins that is defended by determined troops. The smart answer (as even the dumbest 2nd LT in the US Army knows, which is saying something) is to surround it and wait for the defenders to starve.
Crossing the river wasn't that big a deal. Both Armies did it on a regular basis in Russia. Large north south rivers are practically the only natural defenses in Russia west of the Urals. The engineers of both armies routinely crossed large rivers with pontoon bridges and that sort of thing.
A much more probable series of causes was as follows;
a. 6th Army was at the end of its logistical tether and had serious shortages of men and material that could not be made up in time. This did not allow it to attempt an operation of this size and scope.
b. If they were that short of men and materiel (and they were), then they damn sure didn't have the resources to successfully assault the city directly. If so, why did they try?
c. This gets closer to the heart of what I believe to be the real problems: Lack of a clear and focused strategic objective (Hitler), coupled with a baffling habit of changing objectives every week or 2 (as in 4th Panzer Army, again, Hitler) and dispersing their efforts instead of concentrating them.
d. A substitution of fuzzy emotional objectives (death to the city named after Stalin!) as opposed to clear, logical, pragmatic military objectives (again, Hitler).
e. Spineless Generals who would not stand up to Hitler and say no. But then, they all knew that would almost certainly get them fired, imprisoned, or shot (again, Hitler).
f. Hitler's unwillingness to listen to his own military professionals, who were actually usually pretty smart. If Hitler had listened to Guderian in 1941 and gone straight for Moscow right off the bat, screw everything else, they might well have won the war right then. But then, all that got Guderian was getting fired for a couple of years. Again, obviously, Hitler.