Zelda dungeons have a simple yet powerful pattern to them; basically you give the player a new problem, then give them a new item to solve that problem, then give them a boss to kill with that item as a final test of their understanding of that item/mechanic. This formula is a really strong and effective way to give the player new mechanics and get them to use and understand them, but there is a problem with this system: buttons (well a couple of problems, but we are only going to talk about the button space one today).
Real quick though, problems such are predictability (you know the flow of each dungeon before you get to it because it is going to follow the same structure as every other Zelda dungeon and everything happens in dungeons) and repetition (how many mechanically similar dungeons has Zelda made centered around the Bow, Boomerang, Bombs, Hammer, Boots...).
When you find bombs in a dungeon you know you will soon be killing a boss by throwing them in it's mouth.
When a player wants to tell their avatar to jump, punch, use a bow, or whatever, they have to input that command. They can do this by pressing a button but the problem is that there are only so many buttons they can press, only so much button space. This means that you, the game designer, has to allocate that space very carefully as it is valuable real estate.
A player has to press a button in order to tell the game that they want to use the Hook Shot, but there are far more items the player can use then there are buttons for them to use to input that desire. The game can only give items 2-3 buttons but it needs to let the player have access to all of them so the game lets the player swap up which items those buttons activate at any given time by pausing the game and going through the game's menu screen.
The ability to pause and change up items is a necessity but that necessity doesn't make it any less annoying for the player to do. Going through a dungeon is going to require a great deal of item swaps each of which interrupt the game's flow and have the player scrolling through menus (which is boring): This puzzle needs the bow, boomerang, and bombs; so equip those. This enemy needs the hammer to be killed so pause and swap that in. You need the leaf and the boots now. You need the Bow, do you still have that equipped? Get out the Hook Shot and the boots...
Windwaker has 9 dungeon items, in addition to 4 bottles, 3 bags (each full of more items), and 3 more story based items. You can only equip 3 of these though so a dungeon that regularly asks you to use 5-7 of these items is going to involve stopping the action and going into the menu screen a lot.
This is one time I found that the touch screen was actually super helpful for the remastered HD version of Windwaker on the Wii U. The Wii U touch screen let me more easily swap out what I had equipped without having to pause the game and go through a bunch of menus. It was still a bit annoying and would cause me to get hit a lot as I had to keep looking away from the action to get the correct item out. The biggest problem with the touch screen is that it asks you to look away from the big screen (which is presumably where the action is).
Going into a menu in order to re-order your items is a workable solution but it is obtrusive and gamic, it breaks the flow of the action and annoying to do. They don't want the player to have to keep pausing and changing their items because they are now facing an enemy that need to be hit with the boomerang and then immediately go back into the menu so they can change it your items again because the next puzzle requires the some other item. If they required the player to use every item in every dungeon the game quickly becomes menu hell. Even if Zelda games wanted to have a lot of inter-item interaction they can't because of the threat of menu hell.
This is why in items in Zelda games tend to be completely forgotten about once you leave the confines of the dungeon specifically made to utilize their very niche mechanic.
I'm not saying this is a terrible choice, they had two bad options and chose the one that was they felt was more fun for the player. But what can we do to try and have it both ways, a lot of items and no menu hell? We can't just add buttons, but what could we do?
You can kinda add buttons if you are making a PC game because you have the entire keyboard to play with, a similar principle applies to touch screens but touch screens come with their own sets of problems.
I would warn against requiring the player to use the whole keyboard and mouse to play the game though (or even expecting them to), as that is a huge mechanical feat on the part of the player. Starcraft 2 lets the player use the whole keyboard but doesn't require it, players can learn more of the hotkeys as they become more immersed in the game and don't have to know it all from day one.
Create more button space artificially
Dragon Age is a game with a whole lot more abilities then a controller has buttons. To try and address this they made it so you had 4 buttons for quickly picking which ability to use, 3 for using an ability and 1 switching between two sets of abilities (for a total of 6 easily accessible abilities).
This still wasn't enough to give you easy access to all of a character's abilities though, so the player still retained the ability to pause and load up a screen full of abilities to use for each character. But by giving the player access to more abilities at once they lessened how often this vexing thing had to happen.
MMO's like World of Warcraft are another good example of a game with so many abilities that they needed to give the players more buttons (even though they has a whole keyboard full of buttons) so they gave the player the ability to cycle through sets of abilities (thus giving them easy access to more abilities).
Do two different items really need to be two different items, or could be combined into one? In one dungeon you get the first part of it and in the second you get the item's upgraded functionality.
I think a good example of two items that could be combined in Windwaker are the Grappling Hook and the Hook Shot (they even have similar names). They are very similar in function (hook something far away and then use that to move around) but act upon different triggers (Grappling Hook works of branches or other places to swing, Hook Shot works off of targets). Combine them so that when you use it on a branch it works like a Grappling Hook, and when it is used on a target then have it act as a Hook Shot.
This combination alone wouldn't solve the over abundance of items in the game but it is an example of how two items could be combined to lessen the need to continually switch between equipped items in the menu.
Zelda games already do a version of this with arrows. You have normal arrows but also fire/ice/light arrows you can shoot. Instead of having them be separate items that the player equips from the menu they have the player switch between them while they have the bow out.
You could expand on this idea to make it so that each item is a kind of grab bad of similarly functioning items that you cycle between between like the arrows (no pausing the game and trolling through menus needed)
Make items/abilities only contextually usable
I've talked about this other places, but the gist is if an item/ability/mechanic needs certain things in order to be able to be used (a target, a door...) why pretend that it is available for use all the time? When an item can't be used it is just taking up button space and if several scenarios have their own contextually helpful item you can combine them under one banner to save on menu time and button space.
Kingdom Hearts has a good example of this. You are able to use several special attacks (Strike Raid, Sonic Blade, Rave, Ars Arcanum...) but which one you can use at any given time is based on how far you are from the enemy you are focused on. So Triangle activates many different abilities but only 1 is available at any given time (based on the combat situation). In this way they give the player access to a myriad of like abilities but only have to give up 1 button to do so.
So many other options
There are a lot of things you can do, but it also depends on how that solution would work in the larger context of the game. Would combining certain items be a problem story or world wise because of why are the various parts of this item scattered around several dungeons (though why are these perfectly working items scattered around in dungeons in the first place)? Is your character smart and mechanically skilled enough to combine them? Would having items that are actually a group of several items make it harder for the player to find the functionality they need right now?
There isn't a single good answer to this but it is a problem that should be addressed. How would you try and fix it?