I think while the system was built with magic as something not required, the challenges and expectations of the system require it.
Its hard to walk that tightrope of balance with magic; Too much, and you are hounded for being too generous. Too few magic items can make seemingly normal encounters impossible.
Overall, I have run both high and low magic games, and I would say the low magic games were the ones the players enjoyed the most. They didn't have x, y, and z magic items to fall back on, so they couldnt just solve everything via violence, and there was that element of surprise when an NPC villain busts out the Staff of the Kraken. (Or whatever)
Low magic works, your players just have to like it to get it to work.
I threw a "yes" because I prefer simplicity vs vulger ammounts of magic items. Allowing a player to play a spellcaster or PCs to find a small cache of magical artifacts (not true artifacts, but strong, useful magic items) after slaying a dragon is totally acceptable. Randomly rolling half a dozen from the DMG makes magic seem more common than Rations. (In a campaign I was in, which was a good campaign, but I am sure we found more magic items than we did mundane things. I am counting the dungeon furnishings. 'Twas fun for a while, but it just became a numbers race.)