Not mentioned above is a key design criterion that changes everything:
A carrier can sail to the area of action. An airbase cannot.
Longer range is always a good thing, as the Zero demonstrated. But in a general sense, carrier aircraft don't want to be hyper-optimized for range in the same way that one would have to for a land-based plane. So for a land-based plane you optimize for weight and aerodynamics, and if that means you have a wicked stall, fragile landing gear and 1/2 mile takeoff run, well, so be it.
And so you get the P-51. By any measure it was relatively light, especially compared to its Navy counterparts. And some models, like the H, were lightened even more. These were not going to last long on carrier ops!
The P-51's wing was selected specifically for low drag, even though it was known the design gave it high landing speeds and wicked stalls. Who cares? Just extend the runway a little and all will be fine. Again, not an option for carriers.
And finally, since you have lots of airbases, you don't really need to design your planes for multiple missions. So the idea of putting an easily-hit radiator full of boiling-hot caustic fluid on the bottom where it's easy to hit and directly under the pilot? Well, don't fly low. Again, the Navy doesn't have the luxury of space, you planes need to be able to survive all sorts of missions.
And this is why pretty much every attempt to make a carrier plane out of one originally designed for land use is doomed. Look, for instance, at the F-111B compared to the F-14A. Or one can read about the struggles of the Seafire.