Not actually true. Iwo had little to no strategic importance. You may be thinking of Okinawa, which was of enormous strategic value.
The American military originally wanted Iwo simply as a potential emergency landing field for American bombers. Highly unlikely that it was worth the price paid. Better to bypass it and let the Japs starve.
A B-29 was more than the lives of the men on board. A B-29 was a valuable fist even with conventional bombs. The Dinah Mite was the first one to land there in an emergency. Over 30 followed.
Keep in mind too that there were certain other advantages in having the island cleared, the airfield operable, and como on the mountain.