From a logical standpoint, it's because Skyward Sword came out in 2011, and the Skyward Strike is a new idea. Also, like Spiritofzant said, the game software would not allow Link to raise his sword above his head.
From a serious standpoint, it's because Link could use the Skyward Strike thanks to the powers of the Goddess, Hylia. Fi is most likely the reason that the powers of the Goddess were in the sword to begin with, and once the Goddess's mission was complete, there was no need for Fi anymore- or her powers. So along with Fi, the Goddess's powers fell dormant and never awakened again. That's my reasoning for the other Link's inability to use the Skyward Strike.