Aviation destroyers really were a thing the US Navy experimented with.
USS Hutchins(DD-476), Fletcher-class. Was eventually built with a standard configuration instead.
USS Pringle(DD-477), Fletcher-class; first US destroyer to launch an aircraft with a catapult.
USS Stanly(DD-478), Fletcher-class. Her catapult was removed in 1943, unused.
USS Stevens(DD-479), Fletcher-class; first US destroyer to launch and successfully recover an aircraft.
USS Halford(DD-480), Fletcher-class. Her catapult was removed in 1943.
USS Leutze(DD-481), Fletcher-class. Was never built with a catapult but was planned to have one.
In the end, they decided it wasn't worth the trouble.