The limits of a small fighter carrier

Would a 10,000-13,000-ton carrier carrying only fighters and radar aircraft be useful?

It could contribute, especially in escort roles, but a somewhat larger mixed-role carrier would usually be more valuable.

The value of a small carrier depends on its mission. A 10,000-13,000-ton fighter deck might add roughly eighteen fighters to a 1920s-1940s fleet, but that narrow capability would consume machinery and hull resources close to those of a more versatile ship. A convoy-oriented scout carrier could keep a small fighter alert while its other aircraft searched for submarines and surface threats. For battle-fleet service, a 15,000-20,000-ton design would make room for strike and anti-submarine aircraft as well as combat air patrol. A small deck can help, but role and opportunity cost determine whether it is worth building.