WW2 CVLs and CVEs were smaller and cheaper. But CVLs carried a smaller air group and were less robust when damaged. And CVEs were slower and also carried smaller air groups. CVLs and CVEs also had smaller magazines and spare parts stowage and maintenance areas.
Two other WW2 CVs illustrate these problems. CV-4, USS Ranger, was slower, much less robust, and not stable enough for substantial upgrade, unlike her Lexington and Yorktown class sisters. Ranger was deemed unsuitable for the Pacific theater until late in the war, when she was kept in Hawaiian waters for training. CV-7, USS Wasp, was less limited than Ranger, but was still insufficiently robust (compared, e.g., to sisters Lexington and Yorktown which sustained enormous damage before finally sinking).
One could compare IJN lighter carriers Hiryu and Soryu to the much more robust Kaga, Shokaku, and Zuikaku. But, as Akagi demonstrated (one hit, one VERY damaging very near miss) the IJN had damage control design and doctrine issues. That said, even with the same issues as Akagi, Kaga was a floating wreck but would not have sunk on her own for some time had the IJN not sunk her. The IJN got it "right" with the very robust Shokaku and Zuikaku, while Hiryu and Soryu were much less robust than their contemporaries.
I'm not knocking the smaller carriers concept, just pointing out that they can also have "issues". And as ranger suggested above, could be less efficient in staffing.
