The Luftwaffe couldn't destroy the Allied troops in the Dunkirk pocket because it was not a force that could effectively do so. It had neither the strength nor the capabilities required to destroy an army - and until the advent of nuclear weapons, no air force did.

The first obstacle the Luftwaffe would have to overcome to destroy the Allied armies around Dunkirk was the relative ineffectiveness of bombing against troops on the ground. Bombers, especially heavy or medium level bombers like the HE-111, were inaccurate tools, scattering bombs across wide areas. They were unlikely to have significant effects against dispersed, dug in troops. This was especially true for German bombers, which typically carried fewer, smaller bombs than their Allied counterparts. Operation Cobra, an American offensive to break out of the Normandy Beachhead, opened with a massed bomber strike on the German defensive lines. Some 1,500 heavy bombers, 380 mediums and 550 fighter-bombers struck the sector defended by just a single German division. They dropped over 4,000 tons of bombs on this area, practically unopposed by German fighters. The outcome of this impressive display of Allied airpower was somewhere in the region of a thousand German dead (plus ~100 Americans killed by bombs dropped in the wrong place). In other words, it took four tons of bombs to kill one man, not a great rate of return. Of course, the troops massed on the beaches would be better targets than the dug-in Germans that faced the Cobra bombing, but this assumes that the Allied soldiers would not seek shelter when German bombers were overhead, and ignores the fact that the pocket was much larger than just the beaches. Remember, the Cobra bombing went in against a single division's frontage, allowing great concentration of the bombers. There were nine British infantry divisions in the Dunkirk pocket.

The second issue the Germans would have to overcome was the fact that the Luftwaffe was not a large enough force to achieve these sorts of effects. While I don't have precise numbers for its strength during Dunkirk, on the 10th August, it had 1,200 level bombers and 406 dive bombers in northern France. Of these, about 900 level and 300 dive bombers were serviceable and ready to use. As this was after a period of rest, repairs and consolidation, it is likely that the numbers available during Dunkirk were similar, if not lower. These forces had to bomb the Dunkirk pocket, attack ships offshore to prevent it being evacuated, and also provide air support to the rest of the German troops in France. While Dunkirk was being evacuated, there were still large French and British forces fighting on in the rest of France. The Germans needed to keep these forces off balance and under attack to prevent them breaking through to the cut-off troops around Dunkirk. Doing so required air support. Even taking those numbers as a maximum, they compare poorly to the forces the Allies deployed during Operation Cobra. The majority of the German bombers were He-111s or Do-17s, which were comparable to the Allied medium bombers. The He-111 had a bombload of about two tons, while the Do-17 had a one ton bombload. The B-17s and B-24s that made up the main part of the bomber force for Cobra could carry up to four tons for short-range strikes like the mission profile used by Cobra. This means that the Germans would be deploying fewer aircraft than the Allied did for Cobra and each of those aircraft would be much less effective.

It should also be noted that the Allies were attacking from established bases with plenty of time to prepare and build up stocks of munitions. Those bases were well within the operational range of the bombers they were using. The Germans would not have these advantages. I and II Air Corps were operating from established bases in Germany, but this put them at such a distance from Dunkirk that they could not make multiple sorties over the beachhead in a single day. IV and V Air Corps were using closer bases, but were largely deployed against Allied troops outside the pocket. Only VIII Air Corps, with two wings of Stukas and one of Do-17s, could be deployed in full against the beachhead. However, the two Stuka wings had struggled to keep up with the German advance - one was based 240 km from Dunkirk, at the extreme range for the Ju-87. This cut down on the number of bomber sorties the Germans could run. The 1st June saw the most German sorties, with about 160 medium bomber sorties and 325 dive bomber sorties across the whole day.

Finally, the Germans would not have perfect conditions over Dunkirk. Cobra went in in fairly good weather at a time when the Allies had practically uncontested air supremacy. Over Dunkirk, the weather often favoured the Allies. Clouds and mist effectively precluded bombing sorties on the 28th and 30th May, with just 75 bomber sorties across the two days. Smoke and clouds also cut down the effectiveness of the bombing on a number of other days. The Allied bombing effort for Cobra was not effectively challenged by German fighters. The RAF and Fleet Air Arm were always able to operate a fighter presence over Dunkirk. They ran patrols over the coast and beaches, harassing the German bombers. While the British fighters could not stop the bombers, they could reduce their effect. Fighters could break up bomber formations or force them to drop their bombs early or off target.