There's a difference between no magic and low magic. I just did low magic. Basically, I allowed half-casters and warlock. Funny thing is, no one took a half caster although we did pick up a warlock a little ways in. We had a barbarian, a monk, a fighter/rogue and a warlock. Played through Phandelver: Shattered Obelisk right from level 1 to level 13. Worked fine.
So, yeah, 5e does work with very low magic parties. But, it's certainly not geared that way. Most groups, IME, have two or three full casters and probably a half caster as well. Extremely high magic gaming.