Yes, they should have. But that was more of the Japanese industrial inadequacy in fighting World War 2. They failed to keep pace in production of improved weapons systems. One example is the substitution of the obsolescent Val carrier dive bomber with the high performance Judy. Production of the existing Val lagged while they brought production of the Judy on line. In the great carrier battles of 1942, the Japanese pretty much had to fight with their existing stocks of Vals.
On the larger end of this, you can look at their naval construction. They hit on a very good carrier design with the “crane sisters” Shokaku and Zuikaku. We hit on a very good carrier design with the Essex class. The Japanese only built the two crane sisters in 1941. I don’t know why they didn’t try to build more; it seems had they devoted the effort, they could have built a half-dozen more. Not that it mattered, though.
We built 24 Essex class carriers, and that was after scaling production back from the 32 we had planned.
So design wasn’t really the problem. It was production.