Wake Island is a small place and during the war it had a small Japanese Garrison of about 4,000 troops. However, a similarly sized island with a similar garrison, Tarawa, had required over 20,000 U.S. troops to capture and cost over 3,000 casualties. Taking a small, defended atoll could be very expensive both in casualties and in opportunity cost for forces that could be committed elsewhere. Invasions took a lot of shipping and landing craft that were always in short supply for the U.S. during WWII despite it's huge production of these items

Islands that the allies DID take by invasion had to be of key strategic importance, especially after Tarawa. Guam, Saipan and Tinian had important sites for runways to bomb mainland Japan. Iwo Jima had value as a place to base fighters to provide air cover for strategic bombing.

Therefore, the strategy which the U.S. employed against Wake was the same strategy employed against other Japanese held places in the pacific. They "Let them wither on the vine", by using an island hopping strategy. What this entailed was first a devastating air raid to reduce the capacity of the facilities. Air Fields and gasoline dumps were bombed. Port facilities were hit and sometimes sown with air dropped mines. After that, bases further towards Japan were captured (ideally unopposed) and from these bases submarines, aircraft and small naval forces interdicted any resupply to the bypassed Japanese garrisons. Without supplies the damage from the air raids could not be repaired, so the offensive or interdiction ability of the Japanese garrisons soon became minimal.

For small islands like Wake, this meant that the Japanese garrison could literally starve, and 75% of the Japanese troops on Wake perished before the war ended. On other islands, Japanese garrisons resorted to agriculture to try to survive the war. Occasionally allied aircraft dropped napalm to interfere with Japanese efforts to grow food. On Wake this was unnecessary since the island lacked enough soil for effective agriculture. In effect, bypassed islands like Wake were like prison camps for their garrisons with the Pacific Ocean in place of barbed wire.