A question for the Historians. Why didn't the western region become the traditional "Han land"?

Because the mainstay of China's economy in ancient times was agrarian, and the environment in the Western Regions was not arable, and was of no use to the Middle Kingdom. The productivity at that time could not manage too large an area. The purpose of the Central Plains in the Western Regions was for foreign exchanges and trade. To the north were nomads, to the east and south were the seas, and to the southwest was the Tibetan plateau. Only one way to the west can be the most effective foreign exchange.