carried off to Babylon: This prophecy came before the prophecy about saving Jerusalem (Isaiah 37:35). Although this judgment and exile seem like a surprising end to Hezekiah's story, the exile of Israel and Judah was always a possibility (Isaiah 10:3–4, 20–23).
The Lord promised to protect Judah and Jerusalem from the Assyrians in 701 BC, but he warned Isaiah that worse would happen if they did not change. God showed his power and reliability by defeating the Assyrians, but the people did not change. The promises of Isaiah 2:1–5 and 4:2–6 would only come true through judgment (4:4).
Until the exile cleansed the nation's wrongdoings (Isaiah 6:5–7), their mission to other nations would not succeed.