Let's look at the problem with air combat in HoI3 before getting worked up about potential solutions.
As I see it, the problem is that the HoI design has always favored land combat, and as a rule treats the air unit almost exactly like a land unit, with the exception that it does not take or hold land. This means that the stacks of units in HoI1 and 2 had a returning role in HoI3. Also, the idea that an air unit operated as a whole entity wherever it went. It also abided by the rule of "less strength, less org = less effectiveness." While this works for a land unit that operates as one entity, an air unit, by its very nature, is far more flexible. In fact airpower is a third dimension to warfare and it's main advantage is flexibility via extreme mobility. So in effect, HoI mechanics limit air units' main advantage by treating them so similarly to land units.
As such, we see that the air unit is quite often beaten to the point of near destruction, especially when encountering the infamous stacks of enemy air units (which is predictable, hence the need to form your own stacks). The entire unit, despite being somewhat intact after even a devastating battle, has to wait for reinforcement and reorganization.
In reality, an air unit does not need to reorganize. If it loses planes, even a horrific amount if them, it doesn't need to consolidate or move into a rear position to reinforce. It has the flexibility to continue to send its remaining planes on sorties. There is no need for an air unit to sit and wait for supplies or to wait for the baggage train to reach the front line.
An air unit fulfills many missions quickly and goes home to rearm. That's about it. Damaged or otherwise unserviceable aircraft are removed from the roster, and it's go time for the rest.
The main point of contention here is the air units most obvious likeness to land units: it's representation in the UI. It's always been a counter that operates as a whole. This mechanic is a huge abstraction in itself since actual air operations were rarely undertaken by a whole group or wing at the same time. Command and control, logistics of the runways, coordination during the mission and tactical considerations simply did not allow it. The reason we have this in HoI is purely for ease of use.
If we want realism, but playability and less clicks, as well as fun, I'd suggest air unit management and combat be transformed to a more fluid regional combat model.
If we set combat parameters regionally, an air corps could be responsible for the airspace in its assigned region. This region could be domestic or foreign, and it assignment should be based on range.
So for instance, I want to bomb Japan with B-29s based on Iwo Jima. I select my air corps HQ, tell it to focus on daytime strategic bombing in x region. It then moves a little graphic or some sort of indicator over that region. Done. Every day whatever planes can fly go there and bomb. Their target depends on the most target rich province and works down from there. Alternatively I can just tell the corps to bomb everything simultaneously, or bomb all resources, or bomb all of one resource, or all IC in the entire region. Every day, my planes split and perform 5-6 bombings, at the same time!
Let's say Japan AI has an air corps based in that region. It has interceptors, so it contests that region's air space. Ok, so my bombers get intercepted. Since we use regional parameters, my bombers are spread out.
Depending on the intercept effectiveness, maybe 30 bombers are intercepted, the combat only lasts 1 hour... and 4 are shot down. The combat occurs on screen and in the outliner, just as in HoI3. There could be a notification but I would turn these off. I'd select the air corps to ensure the planes were replaced.
Say I forget about this ongoing mission for months. I can set a monthly or weekly report to pop up and tell me how I was doing. If I take a lot of losses, I can cancel the mission or tell the corps to halt when at a certain strength using a slider. Or I could add some long range escorts to the air corps and they'll automatically engage the enemy fighters, thus hopefully lowering my bomber losses.