Lets say you find a setting you want to set your next DnD campaign in, but it's a setting with no magic. A good half the classes use magic, so so how do your address this? Do you just add magic, just not include wizards? Don't worry too much about the answer. It's a discussion not a actual problem to solve.
5e works beautifully as a low magic or no magic game; it's all I've ever run with it and I frankly see no reason to run it any other way.
Certainly, some assumptions needed to change in my games, and players/PCs need to approach many situations quite differently. But there is a host of literature that approaches settings from this perspective, which can be a great guide.
When I run 5e, I use the Primeval Thule setting as a baseline, integrating aspects of the World of Xoth. It's very Sword & Sorcery, very Conan/Fafhrd & the Mouser esque.
I ban all full casters except warlocks and all magic-using subclasses of other classes. As others have noted, this approach leaves plenty of character class/subclass options. In my games monks are a goblin tradition, which adds some interesting background to any character that wants to follow that path.
I DO allow the Ritual Caster feat, as well as Magic Initiate and the feat chain stemming from it that was in one of the playtest packets. I also add the Ritual tag to Magic Circle (why wasn't it there already?).
Now, I don't go NO magic (obviously from the above), and I still have some magic items, but my approach is that any item with a name (i.e. Flame Tongue) is unique and there is only one of them in the world. More generic items (arrows +1) are non-magical, so they might still provide an attack and damage bonus but do not bypass damage resistance/immunity.
I've run three campaigns this way since 2015, with a total of 11 players, and the campaigns were awesome. The biggest was Tomb of Annihilation, which was also the only "official" one I used in its entirety, and all were roaring successes both in my opinion and according to the players in them
Especially if you've already put a bunch of money I to 5e books, there's absolutely no reason to pick up a different game to do what you want here. It works fine.