Tony Vargas
Legend
Sure, it's a low magic setting if the NPCs &c out there don't get much magic. It's just still a high-magic game, if the players choose a bunch of full casters (and that would certainly be a powerful choice on their part).In short, if in your game PCs are regularly slinging spells left and right, and the world around them doesn't bat an eye, the setting is not in fact "low magic", no matter how few NPC casters there are.
I guess that's some ludo-narrative dissonance, there or something.

And, yes, I agree that if you don't want the PCs to be special, and do want to run a low-magic setting, you'll have to force the PCs to conform and be similarly low-magic. That's just not something 5e (nor most other eds of D&D) lends itself to.