Attempting to open the door here will cause King Rauru to turn up again and tell Link that there's actually a fourth shrine on the Great Sky Island.

Source: https://gamerant.com/legend-of-zelda-tears-of-the-kingdom-tloz-totk-closed-door-walkthrough-temple-of-time-shrines/

One of the key narrative components of The Legend of Zelda: Tears of the Kingdom's surprisingly great story is Link's new arm, bestowed upon him by Rauru, the first king of Hyrule and the leader of the Zonai.

Source: https://gamerant.com/zelda-tears-of-the-kingdom-link-arm-rauru-give-back-traversal-abilities-future-games-bad/

The Legend of Zelda: Tears of the Kingdom introduces Rauru, the founder of Hyrule, and his inclusion is reminding players of Ocarina of Time.

Source: https://gamerant.com/zelda-tears-kingdom-rauru-ocarina-of-time-connection-link-past-travel-hyrule-history/