The only point, initially, to the air battles from the German perspective was to gain air supremacy. Without complete and utter control of the skies, Operation Sealion was doomed to failure and the concept of victory by bombers could not be realistically attempted either.
Of course, after Sept., the weather precluded any realistic invasion anyway so the air war continued as it was one of the few ways to take the war to the British (the others being in N. Africa, and most significantly with the U-boats).
Even had air supremacy been acheived by the Germans, victory in Operation Sealion would not have been maintained forever; especially as most of Great Britian was out of range of the German fighters and the allies could safety operate there without fear of German attacks. With lend-lease from the USA, the chance for air supremacy was essentially over by the time (perhaps May 1940) Operation Sealion could again be considered.
I once read that one reason for the German invasion of the Soviet Union was because the Germans had no other strategic options for victory. While I disagree with this, it is true that in Spring 1940, there was little else for the Germans to do. N. Africa was never going to be decisive; summer is not the best time to ramp up u-boat attacks due to the long summer days making submarines easier to spot by airplanes and destroyers, and clearly aerial bombing was insufficient. And with the ever-increasing supply of material from the USA, the UK would only be getting stronger.