Actually, the original 1947 National Security Act clearly transferred the functions of the Army Air Forces to the Air Force. This resulted in Air Force TACPs continuing to exist after the Second World War ended and being somewhat available (not enough of them) on the day the Korean War broke out. The actual problem, other than the A-10 and perhaps the F-4, is the Air Force hasn't asked for a jet powered aircraft suitable for preforming the CAS mission.I think it goes back to the Key West Agreement, the army wanting to have its own CAS.
As the Marines had their own support aircraft, they retained a CAS mission which they performed in Korea, Vietnam and other contingencies/conflicts. This is why the F-4 can be considered a somewhat suitable jet powered CAS capable aircraft.
Scrutiny of documents during period 1947 thru ca. 1955 shows doctrinally CAS was split between support the Army and support guerrilla forces. The CIA was claiming functional control of CAS supporting guerrilla forces under the Special Operations umbrella it inherited from the OSS.
This political infighting regarding CAS to include airlift CIA needed resulted in the demise of the joint service Military Air Transport Service that was initially commanded by an Admiral until the political infighting resulted in the 1948 Key West Agreements, the 1949 National Security Act and other changes. It also resulted in the establishing of what is commonly known as Air America and similar CIA run or funded aircraft organizations supporting their operations.
The summary provided is extremely simplified, but the Air Force has never really vested properly into providing CAS regardless of the Key West Agreements.