Why a ship carrying smaller warships rarely pays at sea

Would a fast ship capable of carrying other warships have changed the Second World War?

Not much; earlier fleets carried small torpedo boats, but modern bases and communications made a vulnerable general-purpose carrier unnecessary.

Concentrating several vulnerable craft aboard one larger target offered little advantage in the Second World War. Earlier ironclads and battleships did carry third-class torpedo boats, giving commanders a way to send small attackers from an anchored force. By the world-war era, better communications and shore support reduced the need for that arrangement. Midget submarines and torpedo boats still used parent vessels in specialist roles, but the concept did not become a general fleet solution.