I remember being pretty resilient when I first got the game, so even though it took a long time the opening moments felt really rewarding for me. The characters become very ingrained in your mind and the mission feels a lot more clear. I also think the gameplay elements serve as a nice way to transition the player from "this is the life of farm-boy Link" into "this is a boy with a justifiable reason to be venturing out into the world". Whole some people call the opening area padding, I see it as a way to ease the player into the world and the story. As for how the material gates itself- I this that's a bit unfortunate, seeing how the game might be hard to get back into with that mindset, but it doesn't really matter much to me. I play games to relax, and I have a fairly decent memory when it comes to the progression of things, so the gated events moved very smoothly upon subsequent playthroughs, it wasn't a source of aggravation. Again, this game does hold a special place in my heart for reasons I haven't yet discussed, so that's just my opinion.
As for the first and second dungeons- the thing I truly love about this game was how, even with its dark and muddy environments and textures, the dungeons are a tour de force of various elements. Rooms share themes but have vastly different geography. In the first dungeon alone you duck in and out of a windy cavern as you solve puzzles, exploring dark, dank portions while climbing on vines and staying out in bright areas. Plus, the monkey mechanic really drives this continuous sense of progression while you also are subtly guided through the experience. In the second dungeon, you have two open areas where you get to flex your skills with the dungeon item, and also wade (literally) through these vertical sequences in your iron boots. It was really fantastic for the atmosphere and Twilight Princess also used it's prerequisite items just as heavily in dungeons as the unlocked dungeon items themselves. Though neither of the two bosses are particularly difficult to defeat, they are suitably spectacular and very enjoyable. It all leads to a pretty thrilling exchange between you and King Bulbin that closes out the story arc for the first part of the game quite well.
Twilight Princess does feel very episodic in nature- there are many mini-stories unfolding in the world as you progress and all of them feel directly influenced by Link's potential and interaction. I think that Ordon and Kakariko are a nice introduction because they feature many of the most endearing characters and story elements. It is vastly different and I like that every area is introduced twice by the Twilight Mechanic- there are parts that feel inaccessible as Wolf or normal Link that are fresh and free as the other, and the idea of banishing the Twilight makes you feel like you've accomplished something as a gamer and a character. I also think that's a good place to end my current thoughts, and I'll return after the next major episode of the story- the path to the Master Sword.