Miyamoto's desire to create a Link to the Past remake was almost a reality.
The Legend of Zelda: A Link Between Worlds was originally meant to be a 3D remake of the Super Nintendo classic A Link to the Past.
Eiji Aonuma told Wired in a recent interview that he "didn't want to make a remake," after being given the task to create a 3D remake of A Link to the Past by Miyamoto, but he wasn't sure how to "incorporate this world into [his] new project."
At the same time, one of his designers "was working on this concept of having Link go into the walls," and, after seeing that, the idea of making a new Zelda game with those mechanics "clicked."
This was all in response to a question about how the top-down Zelda-style levels in Super Mario 3D Land were well liked by fans, and Aonuma confirmed that Miyamoto himself came up with them.