There were several overlapping reasons for the paucity of inline engines in the Pacific War. Firstly, both the IJN and USN made decisions in the interwar period that favored air-cooled radial engines for carrier operations. The USN in particular found that radial engines were more reliable, less maintenance-intensive and rugged than inline engines. The latter quality was important given the rough conditions of take off and landing on a carrier. The USN also discovered that stubby cowlings allowed for better visibility for landings that was not present with the long noses of inline engines. The net result of this early experience was that the US became firmly wedded to using radial engines for its aircraft.

The predominance of radial engines among the Japanese was due to these factors plus the fact that Japanese aviation industry could not reliably produce inline engines in sufficient quantities. The major Japanese inline engine, the Aichi Atsuta, exemplified the problems the Japanese had producing inline engines. This engine was a licensed version of the German Daimler-Benz DB 601 and when it worked, it was a good aero engine. The problem was that Aichi could not produce a long engine crankshaft to the fine tolerances needed for such an engine. In service, the Atsuta proved persnickety and the rough conditions at the front like New Guinea exacerbated these maintenance issues. The aircraft that used the Atsuta, the Ki-61fighter and the D4Y dive bomber eventually were reengined with more reliable radials. The limits of Japanese aero-engine industry's to machine crankshafts of sufficient quality and quantity meant that they relied more heavily upon trusty radials.

Finally, inline engines were not completely absent from the Pacific theater. The RAF and RN used inline engines for its single-seat fighters. In the latter case, the vagaries of British military procurement meant that the RN often had to rely upon converted air force aircraft like the Fairy Battle (turned into the Fulmar), the Sea Hurricane, and Seafire. USAAF aircraft also used inline engines and the combat conditions of the Pacific theater were advantageous for the early generations of US inline engines. The low-level and mid-level altitudes of aerial combat was where engines like the Allison were at their peak performance, unlike the high-altitude combat of the Northern Europe. The P-38 exemplified how different operational factors led to greater success in the Pacific as opposed to Europe. The P-38 was not an enormously popular plane for USAAF pilots in Europe, especially those flying the escort missions over Europe from the UK. Hub Zemke, who flew P-38s, -51s, and 47s, has a very good dissection of the P-38's vices and virtues:

-38--Though this aircraft had virtues, for me it was the poorest of the three US Army fighters in the European Theater. The fact that the extreme cold at altitude affected its performance hardly endears the machine. The turbosuperchargers were controlled by an oil regulator. At altitude the oil had a tendancy to congeal, which cause serious problems. On two occasions I recall, when entering combat with enemy single seaters it was a case of life and death to get away and survive, though I had started with the advantage.

On both occasions the engines either cut out completely or overran rpm limitations as the throttles were cut or advanced. It was enough just to regulate the engines and control the aircraft without entering combat.

The second serious limiting factor that detracted form the P-38's combat capability was its steep diving restriction--estimated at about 375 mph. A common tactic of the Luftwaffe single seaters was to split-S for the clouds or the deck. Oftentimes their head-on attacks on the bomber formations saw them roll over and dive for the deck to confuse and outdistance the flexible machine gunners. P-38s had little chance to pursue. When on defense, it can be easily understood that a dive to safety was the best maneuver for longevity.

Another factor to degrade the P-38's combat capability was the identification factor. The eyes of a pilot often picked up specks in the distance that could not be immediately identified as friend or foe. These were reported in as "bogies." Appropriate tactical maneuvers were taken to prevent bogies from having the advantage of a subsequent attack. In the case of the P-38 the twin booms and slab elevator gave this aircraft's identity away- as far as the eye could see.

It was also necessary for the P-38 pilot to do much more weaving to look down over the two engines that lay on each side of the cockpit. A better cockpit heating system could have been provided as my feet always froze at altitude.

Taken alone, the above statements would conclude that the P-38 had no outstanding features... it did! As a gun platform, it was steady as a shooting stand. With two engines there was no torque. With a little trim for buildup of speed (in a dive) a pilot could ride directly into a target.

As to the armament installation, I have seen no better. Four machine guns and one cannon in a tight pocket directly in front of the pilot. This armament being so closely aligned to the sight of plane of the gunsight required no convergence of fire as necessitated in fighters having their guns placed in the wings.

Though the P-38 had a wheel instead of the proverbial stick, this was no handicap- controls were light and response was excellent.

Relative load carrying capacity, the aircraft could take off with just about anything. I've taken off with a thousand-pound bomb under each wing and cruised with ease. On fuel consumption, the P-38 enabled us to cruise out to combat areas deep in Germany without the anguish of not having enough "petrol" to return home.

A tricycle landing gear made it much easier for a junior pilot to "spike the kite" on the runway and chalk up another landing. This was also an advantage in taxiing- a large engine and cowling did not deter from forward vision.

Note that a lot of the virtues Zemke lists of the P-38- range, load-carrying, heavy armament, good-low and medium altitude performance- were excellent virtues for a fighter operating in the Pacific theater. Even something as ergonomically mundane as a wheel instead of a stick helped aid the pilot in long Pacific sorties by lessening the pilot workload. Nor could the Japanese emulate some of the same tactics as the Luftwaffe. The lighter Japanese aircraft like the A6M did not dive terribly well. The October 1944 US technical report on the A6M5 noted that "the 'Zeke' is a most unpleasant aircraft in a dive due to heavy stick forces and excessive vibrations."

Sources

Lundstrom, John B. The First Team Pacific Naval Air Combat from Pearl Harbor to Midway. Annopolis: Naval Institute Press, 2013.

Peattie, Mark R. Sunburst: The Rise of the Japanese Naval Air Power, 1909-1941. Annapolis, Md: Naval Institute Press, 2001.

The superiority of the inline engine was supposedly proved by the Schneider Trophy contests, in which governments encouraged aircraft manufacturers to enter advanced designs in lieu of military orders which they couldn't afford. Additionally, in Europe the First World War experience meant long range was not a prime design requirement.

To the US Navy, the radial was more reliable, a known quantity, and allowed a greater degree of standardisation on board carriers. The US did more in the 1930s to improve radial engine aerodynamics than the Europeans, among whom they went out of fashion for high performance aircraft. Outright performance was secondary to reliability in naval operations. For the Japanese, these considerations were added to their lack of an indigenous inline engine.

Of course, the Europeans quickly realised their error and designs like the Fw-190 and Lavochkin La-7 were radial-powered. It must be remembered that the world went to war with aircraft designed between 1933 and 39, so the prevalent thinking at this moment was what applied when mass war production began.

/u/kieslowskifan gives a good answer and hits on most of the major points. Radial engine also allow a fighter plane to be shorter in length, nose to tail, than a fighter plane designed with an in line engine. This is an important consideration in the constricted space available on an aircraft carrier.