Reason I believe Breath of the Wild takes place after Minish Cap

I'm using context from the game trailers, as well as this passage that was translated from a piece of art from BotW Master Edition.

"Hylians pass stories of a destined time long past, where multiple races lived and worked together in harmony. The Sheikah Tribe's blue aura breathed through the land, and this mutual prosperity continued, until a cataclysmic disaster struck. The hero and the princess attempted in vain to seal the terror, which became known as the Calamity Ganon. Divine Beasts awoke from four directions, and deployed a mechanical army which made the king and his people fearful. They fractured Ganon's power and sealed him ... But the Sheikah were banished from the land ever since."

*From the fact that the Sheikah Tribe was banished alone, we know this must take place before OoT, as the Sheikah had already been banished for hundreds of years.
*"...Which came to be known as Calamity Ganon." The way this sentence is phrased suggests that this threat didn't have a name until this point. If this game took place shortly after Ganon defeated Link, his name would still be known. Which brings me to...
*"The hero and the princes attempted in vain to seal the the terror." This could suggest the Imprisoning War, but we know the Seven Sages sealed him in the Sacred Realm, and this suggests otherwise. Unless this is a retcon, I don't think this is the Imprisoning War that leads to ALttP. Once again, the Sheikah had also taken part in sealing Ganon. By OoT, the Sheikah were extinct, aside from Impa.

-Why I think it takes place after Minish Cap and directly after Skyward Sword-
In Minish Cap, we saw a relatively small Hyrule, mostly due to the limitations of the GBA. Now we saw portions of established provinces that would be in OoT, but they were small, compared to those in OoT. What we saw was Hyrule in its then current state: a small kingdom. In Breath of the Wild, we know the Hyrule royal family is firmly established, but the land of Hyrule looks mostly untouched, as if it was owned by the Wild itself. While it is possible this could be a SS sequel based on the fact that there's a wild frontier of Hyrule, the fact that the royal family is established leads me to believe that this will take place after Minish Cap.