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Paratroopers weren't used in the majority of the Pacific landings. The islands attacked didn't have enough strategic depth to make it worth using them. In the European theater, during Husky, Overlord, Anvil and Varsity, paratroopers were used to block the approaches to the beachhead (or bridgehead in the latter case). This prevented German reserves from moving forwards to interfere with the landings. In the Pacific, these reserves did not exist. Dropping paratroopers behind the first line of defences would be unproductive and pointless, as they wouldn't be strong enough to destroy the defensive positions. The German air assault on Crete shows how difficult it is for paratroopers to take on troops in defensive positions, especially when the paratroopers don't have a landing zone free from enemy troops (which would be similarly difficult to find on the typical Pacific island). Marine paratroopers did fight during the campaign in the Solomon Islands, but they did so in the traditional light infantry role. Army paratroopers did make a drop onto the island of Noemfoor, but this was after a landing had taken place. Airmobile troops were also used by the British in Burma, where there was sufficient strategic depth to make airborne operations worthwhile.
The Imperial Japanese Navy had several elite infantry units known as the Special Naval Landing Forces (SNLF). Several of them were trained in paratroop duty, and notably conducted airdrop operations in several battles in the Dutch East Indies. Their primary deployment was as blocking forces in conjunction with landing troops to inhibit enemy movement and to cutoff forward units. They were never deployed in large numbers owing to their small size and after the DEI campaigns were reorganized into more traditional land combat units.