That's the thing: 5E actually handles low-magic pretty well
It's OK with low-magic in the sense of not many magic items, or even in the sense of not very many NPC casters. You could easily run Standard D&D in a setting like Primeval Thule that way, for instance - the party may have tons of magical resources, but they encounter relatively little magic in the world.
But low-magic in the sense of no full-caster PCs, that cuts out half the PC options (8 wizard sub-classes, 7 cleric, 2 each Bard & Druid, 2 Sorcerer). And no magic, in the sense of no PC magic-wielding classes at all, the game's not just lacking choices (only 5 non-magical sub-classes in the PH), it's non-functional.
but there aren't that many martial classes to deal with.
And they're all pretty heavily focused on DPR.
(And most of the 4E "Powers" were pretty samey when you got down to it; just bigger dice and modifiers were involved).
Even if the Fighter's 400+ maneuvers over 30 levels were 'really just' 130 maneuvers over 10 with different dice/modifiers at different tiers, that's still a still a whole lot more than the Battlemaster's 17 or so maneuvers at 3rd and nothing else.
Archetypes and Backgrounds allow the customisation.
As Builds & Backgrounds (& Themes) did.
It's not just a question of raw number of choices (which remain paltry even if you use UA & SCAG), but of the resources & contributions you need to have a functional adventuring party (which hasn't improved noticeably).
5e has a lot going for it. It delivers the ol' classic feel of D&D in the 20th century really well. There's not much you could've done with a D&D character before 2000 that you can't do in 2e, and plenty more besides. But compared to the sheer volume of choices in 3.5 or the breadth and viability of martial choices in 4e, it's still falling far short. There's nothing systemic keeping it from getting there, it's just a matter of offering more optional material.
In 4E, there were four martial classes:
* Fighter
* Ranger
* Rogue
* Warlord
The Fighter and Rogue remain as martial in 5E.
Apart from the fact that both can literally cast spells (EK & AT).
The Fighter killed the Warlord and took his stuff.
The fighter might have made off with some of the Warlord's pocket lint.
Perhaps more to the point, the fighter threw away a lot of his own stuff: the 5e fighter is a DPR 'tank' - toughish Striker in 4e terms, like the Essentials Slayer was.
The Fighter also killed the Martial Ranger and took his stuff,
If the fighter simply got a little more non-combat stuff up-front or in each archetype (if each archetype had Expertise in a skill or two, for instance), it really could stand in pretty well for the functionality (DPR with strong wilderness/dungeoneering skills) of the Ranger. It is essentially a striker, afterall.
if you use the UA Scout archetype.
Or, heck, Outlander.
The fluff is willing, the crunch is weak.