The opening is one of the reasons I consider LTTP to be the most "perfect" expression of the basic Zelda formula of any game in the series.
Of course, I think it would be difficult to replicate the sheer efficiency of LTTP's intro in part because 3D games by their nature require a bit more explanation of everything you can do in a 3D environment.
In spite of the hate it got, I actually thought Skyward Sword's intro was the second best of the 3D games, as its "tutorial" act is actually important for the overall plot of the game and setting up characterization for the primary cast members who remain relevant for the entire game.
My favorite start-up section for a 3D Zelda is The Wind Waker; I like the Forsaken Fortress, go figure, and felt that TWW came very close to the LTTP ideal but translated into a 3D and physically larger world.
At the time I though WW was close to LTTP in terms of ideals, but I think SS is much, much closer, mainly because the underworld is pretty much LTTP's overworld in 3D. It's filled with stuff to do and enemies to fight instead of the usual "empty" overworld and the art style is also very reminiscent of LTTP.