Alfred, you are of course correct in some of the cases. The air superiority of course lies in Allied hands here as, I think not mentioned before, the base has been destroyed and kept that way by constant bombing. So only LRCAP is a solution. And in this case sweeps do clear even a pretty large LRCAP as there A LOT of planes sweeping. So yes, it's quite possible to clear enemy resistance provided enough planes are used for sweeping, around 200 hundred will easily clear or wear down an LRCAP of twice or more fewer planes. If not one in turn, then two turns is pretty much enough to do it, provided you employ a large enough force to do it in comparison to your opponent and that's exactly the case. Not to mention, sweeping usually costs the defender much heavier losses than the attacker because of how engine and altitude advantage works.
The problem with your suggested escort solution is of course that escorts get hit badly, very badly, making any bombing runs not really worth it. So nope, escorts don't really tackle the enemy cap. Sure, the bombers may get through but at what cost? Please, you know well that escort missions are not a good solution against even a mediocre LRCAP and just lead to heavy losses among escorting planes. While this is usually acceptable in naval strikes (esp. if the target is juicy and you just need to get through once), you just can't sustain this turn after turn, after turn of land bombing. Your losses will be expotentially higher than these of your opponent making it not worth it.
Anyway, sure, the Allied player earned superiority by destroying the airbase and keeping it this way, but in this case, why would the Japanese player be unable to sweep over it? Yes, I know it's coded this way, but it's one of those things that could use some tweaking I guess (same as nighttime 4e bomber gunner efficiency) though I know this won't likely happen in this iteration. And of course, creative solutions are available, same as sweeping one hex from the base to draw the LRCAP out but it's still not the same and the Allied player is enjoying quite an advantage over the Japanes base because the Japa player just can't use the same means to deal with enemy planes, making bombing very costly if not impossible.
I'm not really expecting that this will change and of course most players are used to dealing with it one way or another, it just strikes me as not entirely reasonable in this case that one player can enjoy an advantage just because of how air missions work. And yes, there are ways to go around it or play the "you hit me and I hit you somewhere else" and playing cat and mouse around the map but it's not really the same.
By the way, you are right that sweeps seek enemy CAP over an enemy base, I know how this works in the game. But why would my LRCAP not engage his LRCAP? Do the pilots from both sides patrol the same area and just wave to each other? :) If you think about it, there are many instances, both real world and gaming, that your cap/lrcap is set over your own bases and engages any enemy that gets close. And in Witp they only engage enemy sweeps, seemingly ignoring enemy planes that are on LRCAP over the same area. That's the problem. And yes, again, I know there are ways to avoid it, not play the enemy's game etc., it's just somehow..weird that you have to do that and cannot enjoy parity in the air mission mechanics at least.