Could you though, really? Like, let's be realistic. If you're making low fantasy you're chopping the wizard, the dwarf, the elf, probably the halfling, I'd say you want to chop the cleric as well. That's already 3/4 of the most basic races and 2/4 of the basic classes. You're excising a lot of stuff right off the bat, to say nothing of how many creatures just aren't ending up used. How many items are being thrown on the chopping floor. So much of the work is being thrown away I'd easily say its at least 80% even when we're talking the most basic books of Basic, not even going into the expanded line.
Yes, you totally could, and we actually did. The great thing about AD&D 2E in fact was that it provided an entire line of historical resource books which you could use to run reasonably authentic adventures in different time periods (Greek, Roman, Viking, Renaissance) and add/subtract magic and other elements according to the rules. So as an example, you could have magic in The Mighty Fortress but it provided rules (clunky, because it was AD&D, but still they were there) for more hermeneutic, slower and methodical magic that better fit the genre. The Viking book ditched regulr D&D magic for a runecasting system. These were fun books for the time. 3rd edition didn't get much of that from WotC, but it was heavily supported with historical references from Green Ronin and others.
Another important difference was that most class builds in older editions did include distinctly non-magical class designs. I am not entirely sure any class isn't at some point using magic or at least fantastical feats in the latest edition.
Either way, as one who cut my teeth on AD&D 1E and 2E, I can assure you that yeah we totally did this and it was also quite doable, and even supported with official materials. And by 3E it was still doable, supported by tons of OGL material. Arguably, its still possible to do this with 5E today if someone were to write a supplement, but the shift in the D&D gamer aesthetic has moved away from tying the game to its origins in myth, legend and history, making this a much more laborious task. (EDIT: and I'm okay with this, because these days I can rely on BRP, Cypher, Savage Worlds, and of course the best resource for historical gaming, GURPS....which by the way was also the best resource during the AD&D 1E and 2E days, too).