I would note that behind the scenes the US ordnance dept did not see the .50 cal as the be-all, end-all of aircraft armament.
There were multiple programs and projects to develop faster firing .50 cal gus which took several years to bear fruit, at least at the standard of reliability the US wanted.
There were also programs and projects for high velocity .50 cal ammo (including necked down 20mm cannon cases) and hybrid .60 cal project/s. These all required a larger receiver than the .50 cal Browning. The fat .60 caliber case was the parent of the 20 x 102mm round used in the Vulcan gun (and the M39 revolver gun, the prototypes that were trialed in Korea as Drgondog states) .
From Anthony Williams website
CALIBRE GROUPS
The 2nd group of cartridges from the 15.2x114 to the 16x99RB were American experimental rounds of the WW II era. Standard .50 is all the way on the left (12.7x99).
The US was interested in high velocity guns in order to simplify air to air shooting, much less lead being needed for deflection shooting.
Unfortunately with the propellants of the time barrel life was extremely short. The standard .50 was hard enough on barrels. Once again
timing is important as later guns got either chrome lined barrels or stellite inserts (or both?) to combat barrel wear.
The High velocity machine guns also tended to be as heavy as 20mm cannon (not surprising as many of the prototypes were rebarreled 20mm cannon.) and the actual increase in effectiveness was debatable.
The US was also trying to introduce what would become the M23 incendiary round, which was a very thin walled incendiary bullet with a large amount of incendiary material that also had high velocity due to it's light weight ( incendiary material being much lighter than steel).
Drgondogs father and friends apparently had some tales to tell about this round when it was being combat tested in Europe near the end of the war.
It was plagued with premature ignition (lighting up in the gun barrels or right in front) all too often and post war it went in and out of production several times and the manufacturing plant changed several times in attempts to solve the problem. Apparently it reached an acceptable state of reliability (or standards were relaxed?) for wide spread use during the Korean war.
The USAAF was NOT trying to fight in Korea with WW II guns and ammo even if they did stay with .50 cal too long.
I would note that the Navy was also not fighting in Korea with WW II 20mm cannon. They were using improved (faster firing) guns and working on more powerful guns/ammo.
