The thing is, the island hopping strategy was akin to a blockade/siege strategy.
When explaining their strategy both during the war and after, a number of US Army planners quoted the famous American baseball player Willie Keeler. When asked how he scored consistently, Keeler said that he "hit them where they ain't." (in short, hit the ball where there was no opposing fielder) The leapfrogging strategy as it evolved over the course of 1942-43 was predicated on the logic that America's growing material superiority would allow the US advance to bypass Japanese strongpoints while invading less-defended areas. These easier targets could then be transformed via Seabees and other construction units into a first-class base that would isolate the Japanese strongpoints and let them wither on the vine.
The most salient examples of this strategy in action was the isolation of the Japanese bases of Rabaul and Truk. American and Commonwealth forces were able to advance on underdefended islands in the Solomon and Caroline Islands like Bougainville, Cape Gloucester, Pavuvu, or Ulithi with relatively light losses and then use airpower and seapower to reduce the neighboring larger Japanese garrison to strategic insignificance. Both Rabaul and Truk had excellent advantages as forward bases in the Pacific, this was the reason why the Japanese seized and developed them, but American material superiority vis-a-vis Japan's overstretched forces was such that it could outstrip the Japanese. Taking these Japanese strongholds would have been costly as they had a large garrison and defenses, but also pointless when the Americans could develop a base that provided the same strategic benefits without having to pay too high of a price in taking it. Japan simply did not have enough men and material to defend every possible island of value, and Allied planners recognized this.
The leapfrogging strategy was as much a byproduct of ingenuity and preexisting strategy as it was an adaptation of circumstances. Although the material disparity between the Americans and Japanese was quite great and grew as the war dragged on, the Pacific was low on the totem pole in the larger American effort. Moreover, there was stiff competition between the Army and the Navy between the resources that did end up in the Pacific theater. The vast size of the Pacific theater also meant that various theater commands also competed for men and material. High levels of casualties and costly victories could risk having either one of the service gain priority or having a theater being shoved lower down the pipeline for reinforcements. Areas that were too large to be taken simply were bypassed or ignored for planning future operations. The British, American, and Commonwealth forces in the China-Burma-India (CBI) theater illustrated the adjustments needed when caught in a theater peripheral to the collective war effort. Although Churchill placed a priority on reconquering all the areas lost to the Japanese in 1942, this was a sentiment not shared by the US Navy, and barely by MacArthur. Thus CBI planning had to shift away from ambitious operations such as Operation Culverin, the planned amphibious invasion of Sumatra, in favor of more practical operations like the invasion of Burma, which culminated in the amphibious assault on Rangoon, Operation Dracula, in May 1945.
Preexisting war plans did help matters out when Allied planners had to come up with solutions to do more with less. The interwar Rainbow Plans, especially War Plan Orange, had already conducted extensive planning for a hypothetical war with Japan and so American planners had a preexisting corpus of potential bases inside the Pacific. It was the Orange planners in the 1920s and 30s that first spotted the utility of Ulithi as a possible future fleet anchorage.
The leapfrogging strategy though was under increasing strain by the last year of the war. As Allied forces entered into the inner ring of Japanese conquests and the Empire itself, they found that the relatively underdefended targets were much rarer to come by than earlier in the war. Shifting political and strategic priorities also undermined "hit them where they ain't." The Philippines could have been bypassed, but MacArthur had placed such stock in their liberation that an American invasion was deemed necessary because of his promise to return. Initially, Allied planners expected to invade the southern island of Mindanao, but intelligence about the underdefended Leyte forced a last minute shifting of the invasion. This though meant that Peleliu invasion was unnecessary as Leyte would be the new staging area, but it went ahead anyway. Japanese resistance severely bled the 1st Marine Division for little gain. Likewise, Iwo Jima was arguably a mistaken invasion given that the planned Okinawan invasion would have provided much the same advantages and the rationale for seizing Iwo had faded. Fighter escorts from Iwo for B-29 missions were no longer as urgent given the shift of American bombing to night attacks and the overall collapse of the Japanese Home Islands' air defense network had rendered much of Iwo Jima's value to Japan quite limited. Credit also has to be given to the Japanese who adapted a more flexible form of defense that made the most of the IJA soldiers' limited capabilities. The defenses of both Iwo Jima and Peleliu eschewed Banzai charges in favor of more prepared positions and tunnel networks.
Although the development and trajectory of Allied strategy on the ground was nowhere near as pat and coherent as Keeler's dictum for scoring, it did work brilliantly for the period 1943-44. Strongholds like Rabaul soon became deathtraps for their garrisons as they were cut off from resupply of food and medicine. To push the baseball metaphor further, bypassed Japanese bases like Truk and Rabaul soon became equivalent of minor league training grounds in the latter half of the war. New Allied pilots would often bomb these bases as part of their operational training, allowing them to practice on live targets with little risk of Japanese opposition since most of their planes were destroyed or out of fuel and AA ammunition was rationed. But the strategy had somewhat run its course by 1945 and Allied planners had to face much tougher choices as to what parts of the remaining Japanese empire to invade and which to leave alone to waste away.
One important reason to capture islands was to use them as bases, both as anchorages for ships, and as air bases. Another important reason was to deny bases to the Japanese. Japanese bases could be isolated and largely left alone, as Rabaul was. The major naval base and airfield complex at Truk was largely put out of action in three days of air attacks in Operation Hailstone in February 1944 (which sank 9 warships (2 light cruisers and the others smaller ships) and 32 transports and merchants and destroyed over 250 aircraft). After this, the garrison, about 40,000 strong, was mostly harmless, and left alone. The Japanese had earlier pulled out many of their major warships based at Truk, and the remaining major warships (cruisers and carriers) about a week before the raid. However, especially earlier in the war, Japanese bases could not always be ignored or knocked out so easily, and were fought for on the ground instead. The first example was Guadalcanal, where the Japanese were building an airfield. The US landings promptly captured the incomplete airfield, which was completely and put into use.
A major goal of the Central Pacific drive (the island-hopping campaign) was bases for the bombing of Japan. China was with range for bombing Japan, and B-29 missions began flying from China in June 1944. However, road and rail links into China were cut (e.g., the Burma Road had been cut by the Japanese offensive into Burma), and fuel and other supplies had to be flown from India, and it was very difficult to logistically support bombing from China. Also, bases in China were threatened by the Japanese offensives during Operation Ichi-Go. A bombing campaign from suitable island bases was much safer from Japanese attack, and could easily be supplied by sea. What was required was islands within range. Saipan, in the Marianas, was the first suitable island, captured in July 1944, and B-29s began to arrive in October. Bombing raids from Saipan began in late November 1944.
Iwo Jima was another multi-functional invasion (which turned out to be less important than originally planned). Japanese fighters were based on Iwo Jima, threatening B-29s bombing Japan from Saipan. Capturing Iwo Jima would eliminate those Japanese airfields, and allow US fighters to be based there to escort the raids on Japan. However, the focus of the raids on Japan switched from daylight precision bombing to night area-attack with incendiaries, reducing both the risk from Japanese fighters and the need for escorts.
The general US procedure was to capture islands where it was thought that bases were essential, or at least useful enough to justify the cost. Early in the war, before the US had an overwhelming naval advantage and Japanese bases could be more easily raided into impotence, eliminating Japanese bases was also important. As US power and confidence grew, and more faith was placed in the ability of carrier forces to support landings, island bases could be further apart. Some islands were captured, and many islands were bypassed. For example, the large garrison on Rabaul (still almost 70,000 strong at the end of the war) was bypassed, 60,000 Japanese were in bypassed garrisons in Micronesia alone (the majority at Truk, but others in the Marianas, Palaus, Carolines, and Marshalls). Some bypassed garrisons suffered badly from disease and starvation (one bad example was the garrison on Woleai in the Carolines - initially 7,000 strong, about 75% starved before the end of the war. The defenders of Truk were well on the way to starvation in September 1945:
