Aren't you all basically passive-aggressively blaming WotC for putting out too many classes and subclasses that use magic? That seems to be the overwhelming theme here.
If your story involves only a little bit of magic, then yes. You are absolutely correct. You only allow the players to select the options you want to have in this particular game.
I'm not being passive agressive at all. I'm flat out blaming WotC for going hog-wild on spells and making nearly every class a caster, and giving EVERY class a caster option.
Flat out. Total blame. Right on WotC.
I think you miscounted. You counted elf one whole time for fighting men, but only a half time for spellcasters.
Moreover, I've seen it suggested in this thread that a 5e class with a magical subclass should be considered a magic class.
By that logic, the ratio of OD&D was 3:3, if including racial classes. I didn't include the races in my original count because, ultimately, they were just the three (well, really two since there were no race class clerics) core classes with a few racial modifications thrown on top. IMO, the races weren't fully realized as classes until BECMI.
I'd say there's just a lot of *magic* in D&D. I, too, often find that a bit distasteful, but in order to keep the game both simple and deep it's difficult to create interesting mechanics that still feel like D&D. That said, I've still never seen anybody play a Sorcerer more than 1 session because the spell selection is so bad (known and list), and weapon attack characters have always dominated every table I've been at.
That said, I've found Adventures in Middle Earth to be a fantastic alternate setting that does a good job of scratching that low-magic itch. There's essentially no spells in that setting. You can take feats to learn a few, but they're fairly weak.
I see the problem, you are creating the campaign and then telling players what they can and cannot do which results potentially in players wanting to play things that do not fit your world. I quit a game a month ago that did the same, the DM invited me, suggested I play a support class as everyone else was covering the melee. I said sure and created a Bard. It turns out everyone else was playing melee because the DM thought magic was OP and had arbitrarily nerfed dozens of spells in the PHB to "fit his world and ideas". I found it less than appealing to play a nerfed character that the DM had suggested and politely said goodbye.
When I DM I talk with my players and get an idea of what they want to play so we do something that in as inclusive as possible to everyone's happiness. That way you do not create a low magic setting and have a player show up with a spell hungry wizard, two others show up with sorcerers, and the last one with his favoite min/max Warlock build.
Designing a campaign for everyone and not just the DM's goal makes everyone happy and results in a longer fuller campaign.