I just finished watching The Pacific and this question kept coming up in my head. For most of the islands the US solders would land and take the island's airfield which was the most important reason for taking the island. While taking the airfields was costly it seemed like the most horrendous fighting came afterwards; the primarily infantry led 'eradication' of the remaining japanese deep in the island who were dug into amazing cave systems in horrible terrain.
What I don't understand is why the US forces couldn't advance just far enough to protect the air field, set up a very strong defensive line and basically just siege the Japanese until they starved. Once the US gained a foothold the Japanese armor and foot attacks seemed ineffective at breaking through a strong US perimeter and the casualty ratio was incredibly higher for the Japanese when the Japanese tried to rush US lines than vice versa. Once the US controlled the airfield the Japanese generally lost naval control of the area and any hope of resupply or air support and without those I don't see how they posed much of a threat anymore as long as they were kept bottled up.
So why did the US military have to make such costly offenses to take the rest of the island rather than just siege and slowly attrition them as they made their costly offensives into US territory or simply starved to death/ran out of ammunition? Am I underestimating how much of a threat the remaining Japanese soldiers on the island were? Would they really have been able to inflict more damage/casualties if the Americans had just played defensively once they took the airfield asset? I understand there would still be casualties in keeping them bottled up, but I find it hard to believe they would be anywhere close to the casualties suffered by going on the offensive and taking out bunker by bunker.
What I don't understand is why the US forces couldn't advance just far enough to protect the air field, set up a very strong defensive line and basically just siege the Japanese until they starved
You posit a reasonable assertion. For the specific situation on Peleliu, the island itself is a mere five square miles in area. This Wikipedia map shows how crowded the island was. After the experience of "sharing" an island with the Japanese on Guadalcanal--in which the airfield was intermittently shelled from the ground as well as repeatedly assaulted--the US was disinclined to repeat the experience.
However, Peleliu was another searing experience for US forces. Immediately after the battle it was referred to as "Bloody Peleliu", and the prominent geographical feature was called "Bloody Nose Ridge." Such vivid references point to how costly the battle for the island was, and that such costs were seen as excessive. While clearing the island quickly was desirable so that the US units could be moved on to another operation, the heavy casualties actually crippled the Marine units involved. The Japanese were using new tactics of digging in and defending in depth rather than defending at the beach itself. These tactics would be repeated on Iwo Jima and Okinawa and would prove costly to American forces.
So why not go with a siege? Basically, artillery range was long enough for the defenders to threaten an airfield, so the defenders had to be removed so the airfield could safely operate. The US did use a long-term approach in the island hopping campaign, but not on a single island. Instead, places like Rabaul were bypassed and left to starve since they could do no harm after being isolated and having their air contingents destroyed. The ranges were just too close to do the same on a single island.
