Tallifer
Hero
I'm not sure how to fit "I can breathe acid" or "I can teleport 25 feet" into racial/background abilities for a gritty, low-magic, humans-only campaign. Saying "I was a wizard's apprentice" doesn't really explain the +2 Str, Fury, and Healing bonuses that seem to come with knowing one "Acid Spray" spell, and also sorta kills the "low-magic" vibe. "I always carry around buckets of acid that I learned to make as an apothecary's apprentice" doesn't really do it for me, either, because then we are interfering with encumbrance and everything else.
I'm perfectly fine with D&D supporting the Wahoo! Its all in there! Mos Eisley Creature Cantina meets the Justice League playstyle. However, I also want it to support the cold, grim Black Company playstyle and the perhaps colder, grimmer Song of Fire and Ice playstyle. I have happily played and ran both styles with several different editions. Some mechanics, be they Racial, Spell, AEDU-power, healing, Critical Hit Tables, or whatever, simply don't support some styles of play regardless of reflavoring. Mechanics do matter, especially in a game as complicated/precise as D&D, even in the older versions.
If you want a world with such little magic, you would have to disallow half the classes as well as well as most of the races. Better to use a different system like Pendragon or Call of Cthulhu whose default characters are non-magical. If I knew how Green Ronin's Ice and Fire game worked, I would say that. (And I do sympathize: I love Westeros. But I would never attempt to play Westeros in D&D.)