If the Zero had had a decent armament and armor, the air superiority would not have switched sides before the end of '44.
But then it would not have been a "Zero" ... In that sense, it had a decent punch - two cannon and two guns, but the design philosophy at the time was range and maneouverability vs armor protection (added weight, which meant less range/ less maneouverability)
At the time, the expected enemy was still flying biplanes, and the monoplanes facing the Japanese weren't that good. By Japanese standards, the sundry Buffaloes, P-36s, (even a few P-26s) weren't a match for the A5M, let alone the A6M (Okay, so the first kill of a Japanese aircraft during the Pearl Harbor attacks was a P-36 shooting down a Zeke ... )
Now, once the design philosophy of the Japanese changed, there were some good designs (Ki-100, etc) that would have seriously challeneged the US airplanes 1v1, but it was a case of too little, too late, and the Japanese lost the numbers game.