The kind of small and cheap aircraft carrier I've outlined would be very cheap to operate. Additionally - they would not be sitting ducks if employed effectively.
For instance, if you have 4 task groups each having a Type 54A, 1 F-22P, 1 Milgem, 1 Damen and say 2-4 light corvettes, and if these were operating 200-400 km from shore, you could have a defensive aircraft carrier placed between such a task force and the shore.
Playing the role of a quarterback supporting these assets from midway.
So, your first line of defense is your task force, with air support, your second line of defense is a light 8000 ton carrier, and your third line of defense is shore-based AShM and FACs.
Task Group A Task Group B Task Group C Task Group D
Light Carrier
S H O R E D E F E N S E S