The F4U did have decent range for a Navy aircraft. But the Navy carrier mission is NOT an escort mission. The Navy generally took off and loitered around the carrier at low power while forming up for a very short time, left on a relatively low-altitude mission (say, 1500 - 15000 feet), and allowed for some 5 - 15 minutes of combat. They typically cruised at 165 - 185 mph, just loafing along.
Escort missions took off and spent some 20 - 30 minutes joining up, cruise-climbed to something like 20,000+ feet. And escorted to Berlin and back at something like 220 mph IAS, which turns into 308 mph TAS at 20,000 feet.
165 mph IAS at 20,000 feet is 143 knots. That turns into 200 kts TAS, or 230 mph. That just won't cut it when flying into combat in the ETO. The P-51s were cruising at slightly over 300 mph and weaving above the bombers. The Corsair absolutely WILL do that, but it won't do it and still retain a good-enough escort range. Yes, they could fit drop tanks. But I don't think the Corsair will magically turn into a good escort fighter.
Would it handle the German fighters? Yes, it would, just fine. But handling the fighters is different from escorting a bomber stream.
The Corsair burned 93 gph at Max cruise at 20,500 feet. Internal fuel was 237 gallons and drop tanks could add another 126 gallons if they were able to be used until dry. Unlikely in the ETO. At a takeoff weight of 13,000 pounds, the range at Navy low cruise speed and low altitude, the range was about 920 NM, or 1058 statute miles. That is at 5,500 feet altitude, at low cruise speeds, with no reserve and no allowance for combat. Straight from the Corsair POH.
So, while the Corsair would have been useful in the ETO, it wasn't ever going to be a P-51 Mustang and tackle long-range missions on a regular basis. That doesn't mean it would not have been welcomed by the fighter community. It would have been.
There are threads in here about how over-rated the P-51 was and is, but I don't see a lot of the people claiming that offering up alternative suggestions for U.S.A.A.F. escort fighters. It absolutely wasn't going to be a Spitfire or Hurricane and, if they WERE available, the U.S.A.A.F. would not have accepted them as regular equipment. The P-47 wasn't up to it, range-wise. Neither was the P-38. We all know the P-39 could do it, at least for 150 - 180 miles or so. Then the P-39 simply drops out of the mission due to fuel shortage. So, it isn't going to make an escort fighter, ever. There were never enough P-61s, and they weren't suitable anyway for escort.
My question is, if the P-51 was so over-rated, what is your suggestion for an alternative U.S.A.A.F. escort fighter? It has to be available when the P-51 was actually available in the war, in sufficient numbers to be useful, and it has to be an aircraft the U.S.A.A.F. would take. That rules out foreign aircraft, which were not really acceptable to the U.S.A.A.F. during WWII.
I don't think the P-51 is overrated in the slightest. It was the only aircraft that could do the job for the U.S.A.A.F., and it was available and in sufficient numbers to make daylight precision bombing, altogether a laughable term ... at least the "precision" part, a reality.
So, they would have welcomed the Corsair, but it would have been used for fighter sweeps, ground attack, support mission, etc. But not for long-range escort.