The A-1 didn't replace the P-47, it was a Navy aircraft. The USAF didn't use the A-1 until Vietnam. The P-47 was replaced in the fighter-bomber role by the F-51, F-80, and F-84. The F-47 would have been useful in Korea, it just wasn't available. Also the range of the Mustang was needed early on when mission were flown from Japan.
The Skyraider did indeed replace the P-47 with it's mission profile in a direct/indirect way.
As for the P-51D, it's max. bombload was 1,000 pounds (divided by one hardpoint on each wing), the P-47D could carry up to 2,500 pounds of bombs max. The F-82 carried a max. Bombload of 4,000 pounds.
The Skyraider could carry up to
8,000 pounds - this also happened to be the max. load/short range rating for the B-17G!
Yes, it was requested by the USN, but it ended up service with the USN, USMC and USAF.
In addition to it's warload and tremendous survivability from ground defenses, it had good range and exceptional loiter time.
And to compare it to the first and second generation jets is apples and oranges.
By the way, the P-80 could carry up to 1,000 pounds of bombs, the F-84 could cary just over 4,400 pounds of bombs and the F-86 could carry a max. bombload of 5,300 pounds, but that would eliminate it's droptanks, cutting into it's range quite a bit.
On the Navy side, the F9F could carry a max. of 2,000 pounds, the F2H could carry up to 3,000 pounds of bombs.
So yes, the USAF may not have "replaced" the P-47 directly with the Skyraider, but in Korea, the Skyraider performed in the exact capacity as the P-47 had done in WWII and again, in Vietnam.