My take is having something that is essentially dungeon tiers. Let's say the game has nine real and proper dungeons. Maybe there's one or two openers like Wind Waker's first foray into Forsake Fortress, but basically I'm thinking you can have dungeons scattered over the world. Use soft gating mechanics like the original game did to restrict the hardest ones but don't hard lock them away (except of course for maybe the last one). Additionally, there should be fun little mini-dungeons scattered around as well. As with Breath of the Wild, you use landmarks and points of interest to draw the player around. Easier encounters can be (for the most part) along roads and more easily traversed pathways while more difficult areas are farther from civilization, hidden away behind dangerous terrain and powerful or numerous enemies. When I think of mini-dungeons, I think of places like the ones you find in Twilight Princess. There were two or three of them that were just these forking paths and rooms that led deeper and deeper. The darkness mechanics of that game really made you feel like you were questing down and down into something dangerous. It felt like real and mysterious exploration. I loved them. But yeah, have a couple of those scattered about. You can keep neat items in some of them, things that make sense for where you find them. So maybe one mini-dungeon is some ancient old Wizzrobe's library or something, so it makes sense to find something like an Ice or Fire rod there. Additionally, use fun lore and world-based context clues to lead players to these places, or goad them into tracking them down. Make the story of the world something that lives and breathes and hides while begging to be uncovered.
But yeah, the tiers idea. So basically you'd have maybe 3/3/3 out of those nine dungeons: three easy ones, three difficult ones, and three very difficult ones. Certain types of puzzles can appear in each tier, so that you can have puzzle and combat concepts that DO evolve through the game but don't maybe rely on some super strict linear guidance. But find a way so that a player should ideally complete at least one dungeon in the low tier before moving up so they at least have a chance to see one or two iterations of a puzzle or enemy type before taking on a much more complicated version of that. Also, use context clues to indicate to the player how strong they should be in order to attempt a challenge. I've voiced this before, but a simple way to do this is to put a few enemies that are in a dungeon in the overworld, very close to the entrance. This does two things. One, if the player suddenly finds monsters they've never seen before, it's a good clue to keep a keen eye on the landscape because there could be a dungeon nearby. The other thing it does is indicate to them if they're strong enough to take on the dungeon. Seriously, if the sort-of-gatekeeper to a dungeon kicks the **** out of you, even if you kill it in the end, the player has the full choice to go "man, this is gonna be really tough, I'm not totally sure I'm ready," or maybe "hmmm, maybe I should pop back to town for some potions and whatnot, then come back. It's tough, but I believe in myself," or "no, this is too strong for me, I'll mark it on the map and come back after a few more Heart Containers, or maybe after I get some new weapon that makes this much easier. That was too much for me right now." Again, this IS NOT HARD. Zelda 1 did this with things like Lynels. Almost everyone who played that game likely found them and got their **** pushed in and thought "yeahno maybe later. I'll check the other side of the map a bit first."
Also, going back to what I said about items like the Fire or Ice rod... don't make items and weapons breakable. I don't want to say I hated the durability mechanic, I enjoyed it for what it was but I don't want it to return. Give me my old weapons system back. But also... don't be afraid to expand items and their uses. Don't do the Twilight Princess method of "one and done"ing items. Make them useful in the world for more than just a few gated Heart Pieces and progression spots. However, if you listened to the podcast on Combat, I brought up an interesting point with weapons. Basically, the designers weren't too afraid to make severely OP weapons like Thunderspears because they knew that you can only be that strong for so long before it breaks. So I get not wanting to give the player too many powerful toys to wreck shop with. My solution is that extra and special items start off really weak. Useful, but weak. Perhaps they serve some sort of utility, like forming little ice bridges, but their strength in combat can be experimental but should be of a power level below your standard weapons. However, through gathering items, information, contacts, materials, and perhaps finding ancient and arcane off-the-beaten-path locations, make it so these items can be upgraded. give them perhaps three levels of strength. And don't make it like BotW's armor system, where you're just schlepping back to the Fairy and going through this horrendously tedious menu to one-at-a-time your gear up to snuff. Make the locations themselves into mini-dungeons. Maybe you find some ancient fount of power and you can channel its energy into your Ice Rod, but to do it you first have to make your way through the Bokoblin camp that grew up around the thing... maybe they have been trying to make it work for their weapons and have been researching it to some extent. Heck, maybe they succeeded, and the boss has some cool attack or ability that sets it apart. Gives you a clue what your reward will be. Just... don't be afraid to integrate the background lore, the present story, the world, and the combat into one.
Anyway, it's hard to wrangle my thoughts right now. I think that's all I meant to say but I'll probably read this tomorrow and find it to be all disjointed and nonsensical...