Actually, the displacement of British armored carriers was determined by Washington naval treaty limits at the time of their design. 23,000 tons was the maximum allowed treaty weight for a carrier.
As for the armored flight deck, this appears to have been the brain child of just one person in the right place to force it through: Controller of the Royal Navy and Third Sea Lord, Sir Reginald Henderson. He was absolutely against the Admiralty's recommendation that repeat Ark Royals be built under the 1934 construction program.
The Director of Naval Construction was directed to design a 23,000 ton carrier with an armored flight deck proof against 500 lb bombs. This was based on an RAF analysis that this would be the heaviest bomb in use for at least the next ten years! Side armor was to equal that of current cruisers.
WAD Forbes, the leading expert on carrier construction was put in charge of the design and then taken out of the normal channels of the construction process and reported to the Sea Lord directly.
The three screw design was the only way the designers could find to put sufficent power into the ship and fit the machinery within the hull size. The design aircraft complement was to be 36 aircraft, half of what Ark Royal was designed to carry.
Another problem found in service was that the armored flight deck lowered the flight deck height sufficently that in moderately rough seas water was being taken over the deck, particularly at higher speeds.
A measure of how poorly the armored carrier turned out for the British can be seen in the fourth and last Illustrious class vessel, Indomitable having reduced armor and a half second hanger deck inserted into the design. The follow-on Implacable and Indefatigable likewise traded armor for a larger hanger and bigger air wing.
The Boyd committee headed by Admiral Sir Denis Boyd towards the end of the war reviewed the armored carrier design. This committee was clearly disappointed by it and felt that a thinly armored flight deck with more armor deeper in the ship would have been a better combination. They also were not kind about the small size of the air wing and felt that much of the damage that British carriers did take could have been avoided with larger aircraft complements.
Basically, within the size and design features of WW 2 aircraft carriers the heavily armored flight deck carrier was a mistake. Air wing size was far more critical as both the Japanese and US correctly deduced.

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