I pretty much agree with Homer. There were important strategic reasons to take the island, all of which had to do with the B-29 campaign:
1. Deny the Japanese a base to mount attacks on our strategic airfields in the Marianas;
2. Deny the Japanese a forward base that would provide early warning of B-29 raids.
3. Provide an emergency landing strip for damaged B-29s returning from the Empire;
4. Provide a base for fighter escorts for the bombers.
However, the ferocity of the land combat was something of an order not seen since Verdun. From that it became symbolic of American determination to take an objective against the bitterest resistance. The flip side was it symbolized the cost we thought we would bear in an invasion of the Home Islands, but on a much larger scale.
PS: You can think of Iwo Jima as our “Stalingrad” experience. Similar type of fighting, only we won where the Germans lost.
Maybe played an important role in the U.S. military thinking that dropping the H bomb(s) would net more lives saved because the war would end more quickly.
The Battle for Okinawa reinforced that in spades.
Iwo wasn't any good for a naval base or Army staging area, but for the reasons you suggest it did have some use as an American air base and depriving the enemy of its use.
I disagree with Howlin' Mad Smith that a few days more bombardment would have substantially lowered the butcher's bill. My god, the Japanese CP was 75 feet underground. We could have taken out a few more installations, but the bad guys were dug in deep. Plus, he doesn't have a lot of credibility with me - he was always Howlin Mad at the Army or Navy or both.