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CAGs and LCAGs should also receive much higher air attack. Since aircraft use their surface defence values against carriers instead of their air defence value, the carriers air attack value is effectively halved since many aircrafts have a much higher surface defence value than air defence value, which is totally unrealistic as the carriers own aircraft would be airborne, attacking the enemy aircraft IN THE AIR and not from the surface.

Historically this was not always true. I think during the Battle of Midway one Japanese carrier was caught with most of its aircraft on deck changing ordinance while the remaining CAG it did have flying had been pulled down to such low altitude defending against earlier US air attacks so that the Japanese CAG was totally unable to interfere in the newly arrived US dive bombers that sank the carrier.

But basically, I agree that the vales for AoD CAGs are not correct, and further there exist other reality problems because AoD CVs are categorized as ships using sea attack value to attack other ships. Obviously aircraft carriers don't fly, but their aircraft don't attack from the surface either. It seems the AoD combat system simply does not have the flexibility to properly represent CAGs and LCAGS either way that combat occurs.

For example, why can CAGs not interdict enemy in coastal province? Because that would be shore bombardment according to AoD - meaning it can't happen unless tied to an ongoing amphibious assault, or there is a beach to make it "AoD possible"? Do aircraft from CVs really need enemy to be in a "beach province" just so they can fly over to attack?

Given the confines of AoD classification, CVs do present a challenge to best set their different values, and Lord Jarski has a good solution to balance one existing problem as per this thread's topic.
 
Another silly thing is that bombing moving ships in AoD is easier then going after stationary ones (i.e. in port): You get +50% naval strike in a 1938 air doctrine tech, but +50% port strike comes in 1941.

Yes, those two techs should get reversed to represent reality and what historically occurred. Sinking ships caught in ports was the first aerial successes and the Japanese did it starting 1937 - USS Panay being only one of the many victims. The British decided to sink the French fleet at anchor after Vichy France occurred because it was so much safer and easier than any other alternative. And Pearl Harbor is a further excellent example of how easy it was to sink "sitting ducks".

But aircraft did not start sinking moving ships until the fine art of dive-bombing and medium level bombing were better practiced and developed. As such Germany probably was the first nation to get considerable success against moving ships, but still "naval strike" was a later development and so should be a latter tech.

Perhaps it is in AoD the way it currently exists because of favorable treatment for Germany's Stukas with too much focus on what threat they were to moving ships. The fact is, they would have been more threat to any ships in port and only their limited range prevented them attacking that way. But still, port strike is the doctrine which was first developed.