Tears of the Kingdom has improved on Breath of the Wild in basically every way, one of which is, providing valid uses for monster parts and other materials! Materials used to simply be used for sale, upgrades, or debatably, elixirs. However, they got a HUGE boost in utility with the Fuse power, which I'll be talking about below!
Quick warning before we start: I am going to be talking about specific monster parts, as well as some details about properties of the Fuse mechanic, so if you want to avoid stuff like that, just keep scrolling!
So let's talk weapons in Tears of the Kingdom then! Weapons generally consist of two components: The weapon itself, and the material that is fused to it. The fused material can be pretty much any singular object or item in the game, including materials or other weapons, or even objects in the world. Regardless of what it is, the material fused to the weapon provides it with a lot of its capabilities and utilities, like whether it can smash rocks, blow wind, maybe its charge attack becomes stronger, or it gets elemental properties. There's a lot of room for experimentation that comes almost entirely from the material that you choose to attach.
Now, for the longest time, I spent all my time searching the world for the right things to fuse-- if I found a boulder, I had to take advantage of it so I could have a hammer when I needed it. But, what took me an embarrassingly long time to realize is, your inventory serves as your arsenal of weapon properties. If you need a mining tool, you can just use a Like-Like Stone, or I believe a Moblin Horn works as well. Elemental monster horns are great for creating elemental weapons! Every single thing you loot increases your repertoire of tools, solving numerous problems BotW had, all at once. If you felt it was hard to justify keeping a sledgehammer around in your inventory, you no longer need to do that, because some materials function as hammers, freeing up inventory space. You also won't regret spending your precious weapons, because some of the most important properties are tied to the fuse material-- not the weapon itself! If you engage in a lot of combat, you'll accumulate plenty of materials, which will only make you stronger in later fights, with no risk of ever becoming much weaker.
Material properties essentially allow you to carry around weapons without using up a weapon slot. You can also learn exactly where to go to get any material you might need more easily than before! Elemental weapons can be supplied in any number of places, from Lizalfos to Dragons. And, if you're fighting a variety of enemies regularly, chances are, you'll never be wanting for any specific type of weapon anyway. It's a fantastic use of the material system. We've gone from Materials in Breath of the Wild being used only for upgrades every now and again, to materials being essential for any and all types of weapon-based utilities you could possibly want.
It's not perfect though-- The developers added a pretty handy material quick-select menu, but there are so many materials in the game now, and the quick-select inventory system is not built to handle it. It's pretty clunky to get out the material that you need, even when you account for the sorting features. Tears of the Kingdom is a game about ready to collapse under the weight of its own sheer breadth of content, and the material inventory is one of the mechanics affected by the sheer scale of the game. It's also complex enough that it might be hard to come to grips with if you're just playing the game for the first time-- I wonder if anyone's still got durability anxiety, without realizing that they may be more well-off than they think they are...
Either way, Fuse is pretty much my favorite power, and enabled so many cool pieces of crafting and experimentation. It's also my favorite sort of crafting system, allowing you to do silly things like attaching guts to a spear, or an acorn to a shield, just to see what happens (usually, not much). I could probably talk forever about it, but I'll be wrapping up my talk re: materials here. It's one of my actual criticisms of breath of the wild, where materials were essentially just kind of useless most of the time. Nintendo's probably put into place the smartest idea they possibly could've for making materials relevant, and it's really fun, too. If you didn't know some of the things I listed here, know that there's plenty more to play with as well, especially to do with Zonai Devices.
If you wanna hear more about my favorite video game stuff, follow my account here! I also stream sometimes, on twitch, under the same name! Happy experimentation and fusing!