If I'm completely honest, I don't really think I want it back, not because I think it's bad (I don't think that) but because it doesn't really do anything particularly beneficial.
All the Stamina did was limit Link's ability to sprint and climb. Imagine having a Stamina Gauge in Assassin's Creed; the game would be unplayable. Zelda is similar in the way that you're always gonna be moving as fast as you possibly can. This is why there have been so many tricks and even glitches discovered to help you get around faster. So to give us a sprint function but then limit it in such a way just stunted the ability to sprint, as far as I see it. Why give us one thing only to limit it with another?
Climbing is another area where the Stamina Gauge didn't do anything for me. Skyward Sword didn't have any areas where you would be climbing for longer than the Stamina Gauge allowed you to. I can see why, it'd be a big pain in the rump to be climbing something and then automatically fall off through no fault of your own, but in the end that just made the Stamina Gauge redundant as far as climbing goes.
So from my experience on Skyward Sword, the Stamina Gauge stunted the welcome inclusion of a Sprint and was completely redundant when applied to climbing. So I suppose I have no idea how they would improve it beyond just getting rid of it. It was a nice idea but I think it doesn't really have a place in The Legend of Zelda.