Exactly what problem did the USN have with liquid cooled engines? The RN had no issues at all it seems. The P-40 likely would have made a good carrier fighter early in the war, possibly better than the wildcat.
The US Navy valued low and medium altitude performance, reliability and low maintenance. Air cooled radial engines were a good fit to these criteria. Furthermore, to the extent that such engines offered high power for a given installed weight, they offered potential advantages concerning the climb rate; this was important for being able to launch and position aircraft favorably to rapidly respond to airborne attacks. The reduced vulnerability to combat damage may have been another factor - the loss of an engine over open water is a particularly unattractive proposition.
The RN seems to have been very happy to acquire and operate F4Fs and F6Fs. They appear to have been surprised by developments in aviation and military doctrine; many of their aircraft at the beginning of the war were hopelessly inferior in performance to contemporary land based types, hence the improvised adaptation of Hurricanes and Spitfires. The reputation of Rolls Royce may have been a factor in favoring the usage of liquid cooled engines in aircraft such as the Firefly and Barracuda, but neither of these types were anything special from a performance perspective. The later Sea Fury and Firebrand used the Centaurus radial in preference to the Sabre and Griffon.