During the game's development, Zelda creator Shigeru Miyamoto had this crazy idea: How about a Zelda game where players cannot see Link?
In the latest Iwata Asks on Nintendo.com, Yoshiaki Koizumi recalled, "First, I talked with Miyamoto-san about how we should make The Legend of Zelda for the Nintendo 64 system, and he asked, 'How about making it so that Link will not show up?'"
According to Koizumi, Miyamoto wanted to make a "first-person game"—something that Nintendo president Satoru Iwata clarified as an FPS.
"In the beginning," Koizumi continued, "he [Miyamoto] had the image that you are at first walking around in first-person, and when an enemy appeared, the screen would switch, Link would appear, and the battle would unfold from a side perspective."
Part of this idea appears to be grounded in the difficulty it was to render characters and backgrounds in 3D on the Nintendo 64. Ultimately, the game was developed and released, featuring Link from a third person point-of-view.
"I was making the model for Link, so I couldn't stand to see my Link not appear," said Koizumi. "Link is cool, so I wanted to always be able to see him."
Nintendo did create FPS tests for internal demos, but abandoned the P.O.V. after deciding it wasn't visually interesting.