Fliegerkorps VIII certainly did try to close the river to Soviet traffic during the Stalingrad battle, but failed for a number of reasons. Firstly, the Luftflotte 4, which covered the Blau offensive, entered in the Stalingrad offensive in rough shape. The strength of the air fleet was some 516 serviceable aircraft in 20 September, when it had started the campaign with 1155. Fliegerkorps VIII was the main ground attack force and it had spent a considerable amount of effort on attacks in the Crimea and Kerch peninsulas. These campaigns were successful, but wore out both machines and pilots. Thus its attacks on the Volga crossings were not at full strength. And like other components of the Blau, Luftflotte 4 was tasked to do too much with too little. In addition to closing the Volga, it also had to cover the Caucasus drive and Voronezh attacks.
Secondly, the aircraft available for attacking the Volga rivercraft were not entirely suitable for destroying these small ships. Experiences on the Black Sea earlier in the campaign showed that barges and small craft were difficult targets and hard to sink through level or dive bombing. To Fliegerkorp VIII's credit, it did manage to close off a significant amount of the riverine traffic by day despite these difficulties, but the Volga flotilla simply switched to nighttime traffic. Attempts to use flares and other nighttime interdiction tactics were largely unsuccessful, and Fliegerkorps VIII instead focused mostly on attacking railheads, river crossing points, and other points in the city. Fiegerkorps VIII's Stukas often flew multiple sorties per day over the city, further straining both man and machine. While the picture on the receiving end of the Luftwaffe was of punishing air raids, each day sapped Luftflotte 4's strength.
Finally, part of the problem with the Luftwaffe's conduct of the campaign was due to command arrogance and errors. Luftflotte 4's commander von Richthofen was arrogant and underestimated the Soviets' capacity for resistance. His war diary in late August complained of "jitters and poor leadership in the army" over the apparently stalled attempt to take the city, and these complaints filtered up the chain of command. The general sense in this period was that air operations were sufficient, when they often in reality were the minimum. Von Richthofen saw a lull in street fighting in early October as a chance to reconcentrate air units for the Caucasus, which further undercut the Volga interdiction campaign. The Luftwaffe also failed to use some of these quiet moments to reinforce Luftflotte 4 from more quiet sectors of the Eastern front. The Torch landings also denuded some of Luftflotte 4's bomber arm as OKL shunted units to deal with this new crisis.
So by the time it had become apparent that there was a buildup for Uranus, Luftflotte 4 was something of a spent force. The autumn rains further cut into operations and the steady tempo of sorties cut down on the overall effectiveness to blunt the emerging Soviet counteroffensive. In contrast to his earlier optimism, von Richthofen's diary entries in November reveal a good deal of pessimism about the future. Luftflotte 4 tried to do what it could to close the Volga, but these interdiction strikes paid diminishing returns as operational attrition and beefed up Soviet defenses took their toll. In the end, the Luftwaffe at Stalingrad was of a piece with the entire Blau campaign; the Germans tried to do too much with too little, and their shortcomings in men and material left little room for errors.
Sources
Hayward, Joel S. A. Stopped at Stalingrad: The Luftwaffe and Hitler's Defeat in the East, 1942-1943. Lawrence, Kan: University Press of Kansas, 1998.
Militärgeschichtliches Forschungsamt. Germany and the Second World War: Volume 6: The Global War. Oxford : Clarendon Press, 2001.
I'd like to mention that air superiority should not imply aviation omnipotence. Air superiority means the ability for aircraft to operate essentially unhindered by enemy aircraft or ground fires; not than an unlimited amount of aircraft sorties are available for tasking.
Even after air superiority is achieved, performing a task with these aircraft then requires an enormous logistical train of fuel, ordnance, parts, as well as a factory of trained individuals to transform those components into repaired, reliable, operational, armed and fueled aircraft for pilots to fly.
Once these aircraft can fly, aircraft are not always going to be the ideal tool for a job. If the issue is preventing boats from crossing the river, that requires constant surveillance of an area in order to conduct armed reconnaissance. (Both finding boats and destroying them.) These aircraft would need to be low enough to the ground to see boats, which means they're (likely; this is an assumption) low enough to be both seen and potentially engaged by ground anti-aircraft fire. If potential river crossings are in a huge area, then a huge amount of aircraft will be needed to observe the river; which is difficult. If only a small area is a potential river crossing area, then that small area is far easier to defend with anti-aircraft weapons, which can harass aircraft and degrade their ability to observe the ground; especially when those aircraft are predictably operating constantly over the exact same area.
It's difficult to maintain 24 hour coverage of an area. You'll likely need two aircraft overhead at all times, with overlapping schedules to account for transit times between an objective area and the airfield, and with backup aircraft on standby in the event of an maintenance issue which would create a gap in coverage. This could be about 60-80 flight hours per day, every day, for months. Each of these flight hours takes up a significant amount of resources, especially when you consider that the majority of these hypothetical 24 hour aerial pickets would be observing nothing and engaging nothing. So that's 60-80 flight hours every day doing nothing, but screening a river, as opposed to actively prosecuting known targets. And, as soon as there is a single gap in coverage, or the Russians move half a dozen anti-aircraft guns into the area for a single hour, a dozen boats move in and the previous week of effort becomes a total wash. My point is, 24 hour screening operations are expensive and come with enormous opportunity cost.
If a screen like this is observed, any logical opponent would then simply...wait until meteorological conditions did not allow aircraft to fly. Night, without a moon or with a slim moon, or a cloudy night, or a number of other factors would be predictable enough to have a known degrading effect on visual observation and render overhead aircraft mostly useless in observing very small dark objects, very far away, or a very dark background.
It's possible for ground observations to control aircraft, but then you're working out response times for a successful interdiction before the river is crossed.
Most likely, it's possible for any individual boat to have been intercepted and destroyed. The Germans had the capability to destroy ships on the river. They likely didn't have the capacity to do so, they still lacked the ability to commit that many resources. Overwhelming air power should not imply omnipotent air power.