Unarmored flight decks (the wooden flightdecks had a un-armored metal banking behind it) were certainly vulnerable, but you have to consider how long it takes to take a ship from planning into production. The Essex class which formed the backbone of the fleet by '43 onwards was basically design frozen in '40. The Essex had an armored hanger deck (which likely contributed to why none of them were actually ever sunk by kamikazes).
Moving the armor layer up to the flight deck had significant weight and balance ramifications (would eat into air wing capacity or fuel/weapons depth) that would make retrofitting existing designs very challenging.
British carriers were armored from the beginning of the war.
The difference in design philosophy can probably be attributed to the British expecting their carriers to frequently be operating in range of superior numbers of enemy land base aircraft (ie, around Europe), and therefore expected their carriers to be repeatedly engaged. American doctrine assumed fleet action, primarily against enemy carrier aircraft, where air wing size would be more useful.
Ultimately in the end, a little bit of both solutions won. The post-war carriers (at least American ones) grew to become large enough to both be armored (by WW2 standards) and have large airwings. But in relative terms... by mid to late Cold War, guided missiles had become large and sophisticated enough that passive defence (armoring) was very much a last chance gamble.
Also, at least in terms of aircraft, while some of the aircraft deployed in the Pacific were clearly woefully out-classed (RIP Brewster Buffalo and Devastator), right from the beginning, many other USN aircraft were qualitatively right in the mix. Certainly the F4F had enough good qualities that USN pilots could wield it at an advantage. The final K:D ratio versus zeros is like 5-7:1 or so, which leads positive for the F4F even trying to account for kill over counting.