Yes the US Navy definitely loved the F4U (and rightfully so), but fearing that there may be problems with it's development asked Grumman for a design as well. Thankfully the "Iron Works" produced an aircraft which at first inception was an outstanding carrier-born fighter, more than capable of providing the needed "muscle" for the US Navy until the F4U had all of it's problems ironed out. Good thing too, because the important battles at Truk, the Marianas, and Leyte Gulf (among others) were all decided by the time the first F4Us were given permanent shipboard duty (seven months after the May '44 report).
During the final year of the war these carrier-based F4Us ultimately achieved less than a third of the aerial victories awarded to shipboard F6Fs during the same period (573 vs. 1734), allowing the "Cat" to take top honors as America's premier carrier fighter once again.
The F4U had to be content with being the more successful land-based fighter of the two designs.
The funny thing was that Corsair was sent to Grumman and helped by them for solve the problems.
But you missed the fact that Hellcat was given much more opportunities. When quoting NASC, you should pay attention to a few points. It was basically pilot's claims in action reports, so it was very exaggerated. Similarly, the identification was also very inaccurate. It's a good reference, but it is inappropriate to treat the kills and analysis against enemy included in it as fact. Some people enjoy to quote a NASC that has not been cross-validated. But it's already proven that it is very inaccurate in the air combat record by many japanese documents. And mostly, they do not consider the situation while saying the NASC figures.
And I think I saw a post like "F4U did nothing for japanese defeat". So I tried to answer that including it.
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Remember that Corsair was a far latecomer compared to Hellcat as carrier based fighter. Mostly, Hellcat had an overwhelmingly superior situational advantage compared to Corsair. Many pilots in the Hellcat had experience in combat for various situations and have a good understanding of how to keep their combat effectiveness in tandem with the fleet. Under the proper control of the Murderers' Row, they boasted a tremendous air-to-air combat efficiency. Corsair did not have those situational advantages. In late 1944, when the Navy built a new squadrons for Corsairs(mostly it's VBF), they had less average experience and skills than the most Hellcat squadrons.
"...products of these changes were the following: the creation of new squadron at a time when the original squadrons had four and a half months of training, with the result that this squadron was far behind the other in training and organization; the assignment of many pilots to the new squadron who had never flown F4U type planes, such pilots being in the majority, and of some pilots who had never flown fighter planes of any type before..."
Of course, there were some squadrons included VF-17 veterans from solomon like the VF-84, but overall, less than Hellcat squadron's average. And VF-84 leaves with USS Bunker Hill, which has been attacked by Kamikaze. And despite superior average combat experience, VMF's marine corsair pilots showed even less efficiency than navy corsair pilots of the VF/VBF at carrier duty in 1945.
While the Hellcat squadrons showed excellent radio communication with good efficiency against japanese fighters, but Corsair squadrons, on the other hand, was surprise attacked and defeated by omitting warning to each other.
"It was a complete surprise attack....(ellipsis)....If they had been alerted and joined in the combat, the situation might have changed."
In addition, during this period, against 343 Kokutai, Corsair pilots reported almost all of bandits as Zeke, Tony, Tojo, and Oscar. But they were all N1Ks. NASC conducted an analysis based on the reported identification. Therefore, there is a doubt about the conclusion.
In so many combats, the level of pilot experience, skill and situational advantage was the most telling factor. In 1945, considering that the action sorties for Hellcat was 2.5 times that of Corsair, So it is to say the Corsair did well her duty despite adverse conditions. If Corsair had more time to gain experience, it would have been able to show full potential.
For example, Hellcat did not surpass Corsair during the period until early 1944, even if it is limited to the period of Rabaul Air War(from 12 october 1943 to 19 february 1944). Because the fleet at that time did not offer the advantage to the Hellcat as much as the Battle of the Marianas or later yet and had less opportunity. Against Rabaul Kokutai the cradle of many top IJN aces, the Corsair was best allied fighter againt best japanese pilots and it's cross-validated now. The Japanese losses included the Dai 1 Koku Sentai and Dai 2 Koku Sentai that were dispatched for the operations, and as a result, their carrier air groups were also got accumulated damage.
At the time after the air raids in Rabaul from the late 1943 to the early 1944, Japanese carrier task force almost lost it's own sophisticated aerial operation capability. Due to attrition warfare, their aviation power rebuilding was not done properly. Particularly problematic was the skill and organization of the pilot. planes was able to supplement, but the pilot's proficiency, experience and organization were not. Since then, the Japanese have been almost silent until the US forces invaded Mariana, for rebuild the aviation power.
Eventually, when the US Forces entered Japan's 'Absolute Defense Line' Mariana and the Japanese dismissed the passive respond and decided to fight. but their aviation power was still not restored. Just before the battle, the training time with their carrier was pathetic.(Admiral Ozawa's Dai 1 KoKu Sentai was 6 month, Captain Jojima's Dai 2 KoKu Sentai was 2 month, others were 3 month) Japanese commanders complained about it. They were concerned about both numbers and experience .
"Surprisingly, SOMETIMES, these pilots did not only take off safely, but even landed, in bright sunlight, in calm waters, without any pressure, without bullet flaring and distraction."
After the battle began, the Japanese air power, which had been lost in numbers, performance and experience, was annihilated. When they encountered the enemy, they did not react properly and were scattered and hunted. In a situation where the organizational power had collapsed, it was best to just survive even an ace. It is due to the fact that the attrition warfare made over Guadalcanal, Solomon, and Rabaul drove Japanese aviation power into a brain dead condition in solomon.
Whereas, when the Corsair was first deployed on the battlefield, Japanese aviation power still remain the ability to inflict sharp damage on the US forces. They concentrated on surviving veterans from previous collapses and maintained their organizational strength. As a result of the cross-validation, actually, they were often victorious in the air warfare over Rabaul. During this period, Corsair shot down highst number of Japanese fighter in allied fighters.(also cross-validated) On the other hand, losses were also high. The Corsair's air-to-air losses were already 50% of the total war in 1943, but the number of action sorties were only 6% of the total war. it indicates what Corsair did at solomons. She fought against better organized and more experienced, powerful enemies as allied main fighter. Although direct damage have been given by bombers, it's a worthy achievement as a fighter aircraft.
After Rabaul, Corsair and Hellcat went a different way. Hellcats and it's pilots were become stronger day by day. They were intensively operated and gained a lot of proactive victories as an carrier based fighter. Also they were could supported by fleet tactics and were able to fight in an overwhelming dominance. After sufficient experience of pilots and fleets, their strength was improved dramatically. it demonstrates the advantages of an carrier based fighter. In addition, The conditions to fight within the advantage against weakened enemies, made it easy for inexperienced pilots to gain experience and victory, So Hellcat became 'Ace maker' and best carrier based fighter in pacific, It's also due to its easy flying characteristics and the high survivability.
On the other hand, the Corsair squadrons were tied to the beach, so it did not get the opportunity as the Hellcat squadrons. While Hellcats enjoy the Turkey shot season, the Corsair gains experience and skill as a mostly fighter-bomber.
By 1945, the two models pilots with different experiences had a generally difference. Marine pilots were regarded as CAS specialists and received a high reputation from ground soldiers such as 'Angels in Okinawa', In Iwo Jima, they taught Army P-51 pilots the know-how about CAS. On the other hand, as mentioned above, Hellcat showed a better figures as an carrier based fighter. due to it's far superior experiences for it.
It is not just the difference in carrier capability. Despite Corsair's superior performance, more opportunities and better situations for Hellcat were made that result. So It is inappropriate to use figures alone without consideration of the situation.
Reference
1. Records of the U.S. Strategic Bombing Survey
2. IJN Zero Battle Diary #2 - victories and losses for Zero over Rabaul from Aug. to Nov. 1943
3. IJN Zero Battle Diary #3 - victories and losses for Zero over Rabaul from Dec. 1943 to Feb. 1944
4. Genda's Blade - Japan's Squadron of Aces 343 Kokutai
5. J2M Raiden and N1K1/2 Shiden/Shiden-Kai Aces
6. 'Vought F4U Corsair' by Martin W. Bowman
7. 'Corsair: The F4U in World War II and Korea' by Barrett Tillman