Not sure what your point is: The island was still built by the Army Corps of Engineers.
The Navy base idea came after Pearl Harbor, when the Navy needed an area to stage its ships before sending them out to war. They requested that San Francisco submit a purchase price. After San Francisco decided that the island was not for sale, the Navy seized it. They then traded Mills Field for the island. (Mills Field eventually became the San Francisco International Airport, which probably would not have fit under the Bay Bridge anyway!)
The city still got to hold its exposition, which is why the island was built. They then got land elsewhere for their airport. It's not like they got screwed, especially since most of the island creation and subsequent development cost was funded by New Deal funds (Works Public Administration and Public Works Administration). The rest was supported by exhibition funds and the local governments.
And keep in mind, that this was during WWII. The priorities were a little bit different then.