In American Caesar William Manchester quites Douglas MacArthur as saying after the Battle of Okinawa: "The Central Pacific command just sacrificed thousands of American soldiers because they insisted on driving the Japanese off the island. In three or four days after the landing the American forces had all the area they needed, which was the area they needed for airplane bases. They should have had the troops go into a defensive position and just let the Japs come to them and kill them from a defensive position, which would have been much easier to do and would have cost less men."
MacArthur was a brilliant general, but his vanity and jealousy of other military commanders were also legendary. Does MacArthur's criticism of the strategy of driving the Japanese off Okinawa make sense? Or were there reasons why MacArthur's approach wouldn't have worked?
That's really more of a military strategy question. No doubt an airfield could have been established on a contested Okinawa. And in general defense is considered more efficient than offense, so McArthur's concept isn't entirely crazy. However, the experience of the Pacific campaign to that point was that the bulk of casualties tended to be on the defenders, and an even more general strategic concept is to not to allow the enemy to be nearby if you can avoid it.
From a more specific (and historical) point of view, one can justify the decision to clear the rest of the island. The remainder of Okinawa had several Japanese air fields and a navy base, allowing for significant ongoing harassment of Allied activity in the area, including kamikaze attacks on shipping. The Okinawa garrison was large and dangerous, and leaving parts unoccupied might allow for resupply, and the Japanese were nothing if not tenacious. This is a recipe for continuous heavy fighting, and far from a safe base of operations (which was the point of invading Okinawa.)