I agree about greatly simplifying inventory down to the most important things, though I'm not set on what exactly that looks like. A few spitball ideas:
1) Never implement crafting. Anything you can craft - just make it something that you can buy. Crafting is very interesting in tabletop RPGs, where you can come up with things from scratch. Crafting in video games, where you're just following recipes, is boring. This lets us remove from the game any item whose only purpose is that it's a crafting ingredient (I'm looking at you bones, spoons, and cutting boards).
2) Anything you find, you can quick-sell (possibly for ~75% of what you would get from selling directly to a vendor). This gives you a way to deal with all of those goblin bows that you don't need without having to drag them around with you. Having them exist as items in the game still allows you to pick one up in the middle of a battle and use it, if you need to.
3) Dramatically reduce the amount of consumables available in the game. The desire for this stems more from class balance issues than inventory management, but getting rid of this stuff would certainly help the latter. I'm fine with having a few consumables, but make them rare and precious.
4) Whatever the mechanism for limiting what you can carry, make it more clear and more engaging. The carry limit shown in the game isn't your actual carry limit; there are multiple stages to being encumbered and they aren't explained anywhere. Someone (maybe Niara?) posted something about this a while back and had good thoughts about it.
5) Give things dedicated places to live. Have keys go on a key ring and/or disappear after they're no longer useful. When you read a book, have the item vanish, but put the text in your journal. Have a little pouch where you keep potions. A quiver where you keep special arrows/bolts. A couple of spots on your belt/back for spare weapons that aren't in your hands.