If used as given... I would assume so. Can DW using it's default play procedures create a gritty feeling game? One where only those who are competent and skilled succeed? One where everyone has a chance to succeed at everything... and so on. And note if your answer is yes, just ignore the play procedures... well we can do that with any game and thus it only really works for those who want the default play style /campaign style that DW offers. When you standardize something you're by nature limiting its possibilities (both good and bad) that's kind of the point...isn't it?
You likely aren't interested in the system enough to self-educate (or I'm sure you would have already), but
here is the SRD and
here is a lengthy, in-progress play by post that should be illuminating.
1) The Powered By the Apocalypse systems (of which Vincent Baker's Apocalypse World is the original) are capable of an extraordinary amount of genre drift. Apocalypse World (as I'm sure you figured out) is a grim, post-apoc set game, kind of Mad Max meets The Road meets Fallout.
2) Dungeon World's default is a Story-Now system that is sort of a mash-up of B/X, 4e, and a smidge of Burning Wheel but it is easily driftable to something like Clinton R Nixon's post-apoc Sword & Sorcery of Shadows of Yesterday.
As mentioned prior, the basic resolution mechanic is a fiction-triggered "move" > roll 2d6 + stat mod > 6 - is a hard failure with major complications and mark 1 xp, 7-9 is success with complications/worse outcome, 10 + is success at intent (outcome-based design to generate the aforementioned bell curve). The basic resolution mechanics, the GMing protocol, and the fiction-first play procedures generate an enormous range of possible outcomes on any given roll of the dice (rather than binary pass:fail outputs, content generation/fiction evolution by way of dice is considerably less bounded in DW). Beyond that:
1) Armor is DR
2) HPs are low @ class (4, 6, 8, 10) + Con and don't change (unless you stat up Con - you get + 1 per level)
3) Combat with multiple opponents gets very dangerous so you have to find ways to deal with that
4) There is no action economy. Again, every move (GM or player) is triggered by the fiction and the snowball effect of the basic resolution mechanic's output.
5) Keyword tech drives a generous portion of the game (Near, Far, Forceful, Messy, etc)
6) There are open descriptor resources that can be deployed to avoid danger or augment your ability to mitigate it (Adventuring Gear uses being a primary one)
7) Magic is quite magical, heroes are heroic, danger is dangerous (and everywhere) and adventure is meant to be generated spontaneously by virtue of faithfully following the rules/play procedures. Play can easily be drifted from the mythical heroics of 4e to the bloody meatgrinder of old school dungeon crawls.
8) But everyone works off the same rules/basic resolution mechanic. In that, there is uniformity or standardization in systemization of play procedures.
Wizards and Clerics
Cast a Spell and roll 2d6 + Int/Wis to find out what happens. Fighters
Hack and Slash and roll 2d6 + Str to find out what happens. Paladins
Lay on Hands and roll 2d6 + Cha to find out what happens. Rangers
Hunt and Track and roll 2d6 + Wis to find out what happens.
You get the idea.
As to your premise of "when you standardize something (i) you're by nature limiting its possibilities (both good and bad) (ii) that's kind of the point...isn't it?" No, I wouldn't say that (i) isn't correct and, accordingly, (ii) can then not be correct. In TTRPGs, uniformity in structure and composition serves a few discrete (yet synergistic when taken as a whole) purposes:
A) It minimizes mental overhead and/or table handling time by simplifying play procedures to intuitive necessaries. You aren't referencing several subsystems or tables that interface with one another. Consequently, this serves as grease for the basic conversation and pace of play.
B) It minimizes the prospects of 2nd and 3rd order effects, happening when dissimilar/discordant subsystems/procedures interface, causing unintended mechanical artifacts to throw a monkey wrench in the system's machinery.
Taken together, these allow players (GM included) to hone in on themes of interest, the conflict therein, genre fidelity, and "playing to find out what happens" as interesting, genre-coherent story can unfold organically rather than being forced.