Just because I like to be a pain:
Well played, sir! You're engaging with counter-examples, rather than complaining about "asshat".
I agree with the part about PCs having *items they care about*. I don't recall anything about Robin Hood's bow being enchanted, or made from The Special Yew Tree that's Super Effective, or anything like that. On another hand, I imagine that it was balanced just right for his arm length and his height, that he tensioned the draw to just the right amount, and that if you took it away and left another bow in its place, *he would notice*. Taran Wander made his own sword. And so forth.
My main 5E PC, in Faerun, has three magic items. All three were gifts, and he wouldn't trade any of them for 10M GP or for a +3 Vorpal Sword, because each gift represents a relationship or accomplishment which matters to his story.
I mentioned Odysseus, but not Achilles, who gets a divinely-forged shield. Robin Hood's LG counterpart is Arthur, who gets Excalibur and its sheath. Boromir's horn might be enchanted. Aragorn has Narsil.
Just because I like to split hairs:
Odysseus had the wind bag rather briefly, same with the moly. Neither was in his "inventory" in Ithaka.
The bow which he uses to kill suitors isn't *enchanted*. But it's special; maybe minimum STR 18 to wield?
Beowulf wielded Hrunting. Perhaps it was a well-made sword; perhaps masterwork. Or maybe just balanced perfectly for him, in the same way that a bowler has their favorite bowling ball with the finger holes perfectly aligned.
Wait, Legolas has two swords? In the LOTR books, he fights with a knife, when he runs out of arrows or enters close combat. Perhaps movie-Legolas is a re-skinned Drizzle?
Gimli, though... Gimli could have picked up any axe from any competent blacksmith's shop and been just as happy and just as effective. If you want his axe to be magic, then I think that says more about your assumptions and biases as an RPGer, than it says about Middle Earth as Tolkien imagined Middle Earth.
Inigo Montoya's father made masterwork swords. There is an excellent scene in which Inigo gets magically guided. That isn't because the SWORD is enchanted. That's because he's using the sword to focus magical power which comes from... well, let's just say a source which originates outside the sword and which acts through it.
Bilbo finds a Ring of invisibility. True dat. It's a big deal. It's not "hey, now that I'm an adventurer like Thorin, I'm starting to get cool items, like the three magic items that Thorin has! When I level up again, will I catch up to the Standard Amount of Magic Items?"
At the end of LOTR, Frodo does not have the Ring; victory is *defined* in terms of not having the ring (and no one else having it either).
The glass of starlight is an awesome magic item. What would it do, in D&D terms? Enable casting of Moonbeam? Nope. It shines, and it renews life and hope, when hope is scarce. Completely consistent with the themes of LotR.
So, what are the themes, in the story told via the D&D game at daddystabz's table? and what magic items would express those themes, with equal beauty and wonder?