It exists because:
1) Aonuma doesn't want to make a game the Zelda fans wanted.
2) The Zelda games Aonuma wanted to make weren't doing well. At least as far as sales goes, Zelda was regressing horribly.
Breath of the Wild is actually the best of both worlds in that regard. By completely abandoning the core values of the series and the formula the original LoZ set up, Aonuma is able to make a game he wants because he is leaving the Zelda formula. The Zelda fanbase as a whole has always been a niche, so instead he is focusing on the much larger fanbase dedicated towards Open World games.
In addition, Aonuma has never been a game. He's never liked working with gamers. He's said himself that he prefers to have non-gamer developers. So this was also his chance to remove the old Zelda development team and replace them with new developers who don't have a gaming background.
I mean, the series abandoned those values years ago. The series stopped being about adventure and exploration and started being about routine and following a specific series of directions with little to no deviation. Heck, the need for a "formula" at all is no doubt partly responsible. No game series should ever follow a formula.