The Corsair remained in production somewhat due to foreign orders, but when the Hellcat was more or less retired ... not really since a lot went to reserve and training units ... they had enough Corsairs around for "spares" to keep them flying for about as long as they wanted to except if they wanted late-model aircraft. After all, there were a LOT more F4U-1, -1A, and -1Ds around than F4U-4s. The Corsair hauled a bit more bomb tonnage and was better equipped for bomb hauling. The Hellcat was never designed for that task, but it certainly gave a lot of reseve pilots some great fun in a peacetime Navy.
My thoughts are they stayed with a proven good performer of choice (could really have been either plane) until jets could catch up with carrier requirements. Once they did, the only piston that stayed in production and service was the Skyraider (I am not counting planes like the S2F since it wasn't a "fighter"), and the Skyraider has been discussed in here at length. It is definitely MY facorite piston attack plane of all times since it is the one that saved my life on several occasions.
Keeping multiple types in service is expensive. You have to train multiple principal mechanics and repair people, muiltiple pilot schools, etc. So once you pick your choice to keep for awhile, you cut costs and draw down the retiring types. Usually they issue them to guard and reserve units untl they become too hard to maintain. By then, there is usually another semi-old type that can be drawn down to guards and reserves.
They are trying desperately to retire the -10 today desite knowing we can't replace it with the F-35. But they have to justify the most expoensive aircraft in history somehow ... that's another story best left to another thread. I'm not sure who wants to risk a plane taht costs as much as an F-35 going after a flak battery, but if they're going to fly them, they have to have a purpose, don't they? The point is, you pick a platform or platforms, support them, and "retire" the supply chain / acquisition / maintenance chain for the types you elect not to keep.
In theory it is cheaper but if you leave capability gaps and then, for some reason or another, NEED the lost capability, it is tough to reactivate it unless you maintain something like "flyable storage." That can be VERY expensive since flyable storage requires regular maintenance. Getting an older plane out of Davis Monthan and returning it to flight status is NOT cheap. And you have to find people qualified to operate, too.
Please don't interpret this as a put-down of the Corsair. No way. The Corsair happened to be the choice made by the people maing the choices at the time. Had they chosen the Hellcat, then we'd be having the discussion the other way.
In point of fact, the F4U-4 was a better plane than the F6F-5 in late 1945. I don't know if the Hellcat could have jumped to new levels of performance had they made major improvements to it, but I'm sure it would have been an expensive development effort to make a Hellcat do what the F4U-4 and newer versions could do ... and the F4U-4 was already in production flying when the war ended, so there is no way to justify developing something you already have. Had I been making the choice of either the F4U-4 and F6F-5, I'd have chosen the F4U-4, too.
Had the war continued, the Hellcats would probably have been in action to the end unless the end was so far down the pike that jets replaced pistons before the end of the war. Glad THAT didn't happen.
I know the Navy crews were glad to get planes with hydraulic wing fold. I know several guys who got thrown 10 - 15 feet on their backs when trying to fold Hellcat wings. If nobody else did, the wing folders wanted the Hellcat replaced or, at minumum, a hydraulic pump fitted! If you get in the way of our TBF Avenger today, it will pick you up and throw you a good, long way and not even notice you were standing there.
Here's a post-maintinace hydraulic checkout.
View: https://www.youtube.com/watch?v=6bh3CKw_HLk
It doesn't LOOK fast unless you are standing where the wing is going. I can guarantee it will FEEL fast when it hits you.
We had a couple of guys run around behind a Skyraider once just when he was doing startup, to get some cool pics ... without asking or even checking with the pilot. The prop blast blew them through 2 - 3 rollovers along the asphalt. Their cameras were both broken and they needed the first aid kit. That was some years back.
After laughing for awhile, we helped them and now put ropes around our planes for crowd control during public events. The public now must stay inside the museum property and they don't even want volunteers out there during public startups unelss you have had fire guard training. Too much chance of having things go wrong for the untrained. If they are just going out for unscheduled flights, no problem if you are one of the people who helps with planes. But for public demos, they want only the crew assigned near the aircraft. Makes perfect sense. You don't see any untrained people on a carrier deck either.