I'm not sure I am following your logic. Mitchel's test proved two things:
1 - Air power alone could indeed sink a capital ship which regardless of the hindsight from today was not widely believed at the time.
2 - Said capital ships were not equipped to properly deal with air attacks.
From that information, at least 2 things can be done:
a) - Continue to improve the ability for airpower to destroy naval targets (which was done)
b) - Improve capital ships ability to deal with air attacks (which was partially done)
The smallest guns the Ostfriesland was equipped with were 14 x 88mm anti-torpedo boat guns and the mounts do not appear to have the ability to elevate to engage aircraft, though I could be mistaken as I cannot find a very clear picture, so zero protection from the air.
At the time of Pearl Harbor the USS Arizona was equipped with 8 x 5" & 8 x .50 MG AA guns, and was going to be equipped with at least 2 x 1.1" AA guns mounts of 3 or 4 barrels each IIRC.
During the Battle of Sanata Cruz Islands, the USS South Dakota was equipped with 16 x 5", 68 x 40mm and 76 x 20mm AA guns.
During Pearl Harbor the Japanese lost 29 aircraft while attacking all the US bases and ships. During the Battle of Sanata Cruz Islands, the USS South Dakota on it's own shot down 26 Japanese aircraft.
Taranto and Pearl Harbor reiterated point #2 above and the raids would never have happened if point #1 had not been proven.
I look at his tests like going to the moon, the first test you conduct is not putting a man on the moon, but seeing if you can even make it into space.
IMHO Battleships still have a part to play, which is why the Russians still field Kirov class battlecruisers. The final refurbishment of the Iowa's were the removal of turret 3 and a flight deck installed for Harriers. Today those would have been replaced with F-35Cs and it would have been a potent platform.