Reread the Simmilarian and tell me that Middle Earth is a low magic setting.
Every member of the fellowship has at least one magic item, usually more, including a couple of artifact level items like Narsil and the Ring. Gandalf goes toe to toe with the most powerful wizard in Middle Earth (Saruman) and while he loses, he does give as good as he gets. Never mind that he also goes toe to toe with a Balrog and wins. Gandalf uses as much magic in the novels as he needs to. Lets not forget that a fair chunk of the Fellowship isn't even human, they regularly face inhuman monsters, and that non-humans are numerous enough that they can actually field armies.
These are all tropes of high fantasy. Low magic doesn't just mean low magic items. Low magic, means that non-humans are incredibly rare, almost non-existent, monsters are more "prehistoric beasts" like giant snakes than immortal spirits riding dragons.
This is a mistake a lot of people seem to make. Low magic isn't just about limiting the number of glowing swords the party finds, it's about a setting where magic is actually rare. Magic isn't rare in a setting where you have immortal elves rubbing shoulders with humans while the forests are full of Ents and were-bears, and dragons hold sway over large chunks of land.