There is nothing unusual about claiming an uninhabited island. It is very common. There even some territorial disputes about islands that include uninhabbited islands - example.

Also just because an island is uninhabited doesn't mean it is useful. For example Midway Island and Wake Island used to have military bases on them. Those bases are not defunct but they could be reopened if needed.

They will extend your (now) legitmate claims over what would otherwise be international waters.

The U.S. claims a lot of islands under the Guano Islands Act of 1856, 48 U.S.C. § 1411-19. I don't know if all of these specific islands were claimed under that Act, but we claimed huge numbers of islands in the late 1800's and early 1900's, because of, you guessed, Guano is great fertilizer.

Some number of the islands that make Pacific Remote Islands Marine National Monument are in fact islands claimed under the Guano Islands Act, specifically Howland Island, Jarvis Island, Johnson Atol, Palymrya Atol, and Kingman Reed/Danger Dock. Some of the islands in the Monument though, I'm not really sure of the origins of, specifically Wake Atoll.

See Jones v. United States, 137 U.S. 202 (1890) for a brief discussion of the history of the act, applying criminal jurisdiction to crimes committed on the islands.