We seem to be confusing a whole bunch of things here.
Air attack was not static from 1921 to 1939 let alone 1942-45.
different types of ships have different resistance to damage. A lot of it is passive resistance and armor is just a part of it.
Counting a carrier like the USS Bismark Sea like a Lexington or Hornet is not accurate. But being accurate calls for very lengthy posts. Also a lot ship battles or ship losses seem to have an element of luck to them, Like the USS Bismark Sea : from wiki so........" The fire was nearly under control when the second plane struck the aft elevator shaft, exploding on impact and destroying the fire fighting salt water distribution system, thus preventing any further damage control. "
Now would a larger fleet carrier have had a redundant fire fighting system at the other end of the ship? If the fire fighting water system remained operational would that fire too, have been extrigwhiched/contained?
USS Bismark Sea was one of the Kaiser jeep carriers and was powered b reciprocating steam engines. Under 11,000 tons full load.
Battleships had hundreds (the big modern ones had over one thousand) of water tight compartments, which made them hard to sink compared to older ships and to cargo ships.
Put out of action is one thing, actually sinking one is a lot harder. Something the submarines also learned, one torpedo hit was usually a mission kill, but it took a lot hits to actually sink a modern battleship that was at action stations and fully manned.
But back to Mitchel and the air threat vs ships. By the mid 30s (and it took about 4 years to build a battleship) Every navy in the world that could build them was devoting hundreds if not several thousand tons to AA defense.
10 US 5in/38 twin turrets weigh about 750 tons and that does not include shell handling rooms, structure to hold them, hull structure to float them the 9000 rounds of ammo to feed them or the several hundred men to crew them (and the berthing spaces and mess spaces they needed and food/water/supplies for these men for several months. And the fire control arrangements.
Something was driving the requirements for such an expenditure or allocation of resources and if not Mitchel and the Ostfriesland trials then it was trials in various countries based off the the Ostfriesland trials (with no old battleship available these could be bomb accuracy trials or trials against a simulated target.)