4e introduced inherent bonuses in place of magical attack bonuses. 4e came the closest to having martial be comparable in the other pillars though it did it by reducing the magical effects available (and then bolstered them with more free form effects with DM fiat combined with page 42/skill challenge results) as much as by bolstering martial abilities (especially if you used a playstyle similar to [MENTION=6696971]Manbearcat[/MENTION] or [MENTION=42582]pemerton[/MENTION]).
If you're running the game in the way that [MENTION=6696971]Manbearcat[/MENTION] or I might, then you won't have a set-up quite like the one [MENTION=23935]Nagol[/MENTION] described in his early post in the thread: for instance, there wouldn't be a timeline that the PCs have to meet in order to succeed; rather, the sort of time-driven pressure/failure that Nagol describes would be an outcome of resolution (probably in a skill challenge). Likewise, the presence of handy water breathing potions in a surface lair would be more likely to be the outcome of a successful check or initial skill challenge, than something preset by the GM.
Quick contribution to the thread (that is, surprise to no one, in line with what Nagol and pemerton have written).
The 5e game I stand-in GM about every 6 weeks (or so) is for a couple of 16 year olds and their mid-40s dads. The regular GM has his own world with backstory and a standard hexcrawl map (1 mid-size hex = 6 miles and a zoom-in to 1:1 mile) with all kinds of adventuring sites. He sees 5e's Ability Check system exactly as I've expressed; the "natural language" interpretation of the Ability Check system is one governed by in-setting causal logic with the common man as the baseline and the DC descriptors (Hard, Nearly Impossible, et al) as one characters would use in-game rather than metagame cues for the players at the table. Therefore, DCs are objectively established and adjudication. Hexcrawl and poor man's process sim. That is how he runs it. Consequently, that is how I run it when I stand in for him (out of courtesy, continuity, and coherency). And I agree with him. This is what 5e has systemitized. You can drift it (and surely run into some dysfunction that will require further hacking), but that is what the game supports.
Success at a Cost (failure by 2) is used but neither Degrees of Failure nor Crit Success/Failure are used. Random Encounter tables are rolled at intervals of 1 hour to 10 minutes depending on the locale. Social Interaction conflict resolution mechanics are used. The Chase conflict resolution mechanics are not used.
Game is 17ish level. I've probably run...a session-ish at each level. The two teenagers play the spellcasters; Land Druid and Enchanter Wizard. The two dads play Totem Barb (Land Druid's brother) and Archer Battlemaster Fighter. There have been a few guest appearances, but that is the main group.
My observations regarding some of the things I've skimmed in this thread:
1) Skilled Hirelings became outmoded long ago.
2) Background Traits have been deployed more and more scantly as the game has progressed (to the point of being nearly outmoded).
3) The Ability Check system see most of its use with the Social Interaction conflict resolution mechanics (so Insight and Cha skills), Perception (generally, but also) vs Stealth contests, grapple contests, some Tracking, some lore/investigation, and to overcome some physical obstacles when the players don't want to spend spells to do so.
The players don't stunt (which would leverage the Ability Check system). I stunt with monsters pretty regularly, but that is about the extent of it a the sessions I've GMed.
As the two spellcasters have had their spell breadth and load-out proliferate, the Ability check system has become less and less relevant to proactive player moves to overcome obstacles in the Exploration and Social pillars or gain resources/assets. It is mostly cordoned off to reactive contests at this point.
Long story short, outside of the Barbarian's Commune With Nature Ritual (still gets deployed for fair utility...still a spell) and Beast Sense Ritual (...still a spell) + Druid Animal Friendship power play, the Druid and Wizard resolve pretty much all of the Exploration and Social conflicts. The Barbarian's Tracking and Stealthiness used to have much more utility for perilous journey travel stuff...but is now outmoded by spellcasting. The Fighter's Know Your Enemy contributed once to parley, Artisan Tool has never been relevant in conflict resolution, and the save rerolls have been brutally sparingly used against wilderness hazards/traps (maybe 2-3 times?...pretty much always used in combat...mostly against spells).
So I've been seing spellcasters being the lynchpin to the healthy majority of conflict resolution (especially noncombat - Exploration/Social). They are pretty much exclusively the obstacle-obviators, the scouts, the unfavorable scene-transitioners (combat or travel), the resource/asset-gainers, the intelligence-gatherers (save for the Barb's Commune With Nature ritual). And they still contribute mightily to the combat pillar with healing, buffing, debuffing/battlefield control, conjurations, and AoE damage.
I think (if you want a player-driven game...not GM-driven via application of force) parity wobbliness toward the end of the "Heroes of the Realm" Tier (half-way through the levels) and onward for mundane characters could be addressed with one or all of the following:
a) Go from hexcrawl (mechanics/scale) of granular map with rigid backstory to abstract/low resolution map with malleable ("No Myth") backstory that gets firmed up in play via action resolution.
b) Change the Ability Check paradigm from objective/grounded + task resolution to subjective/mythic + conflict resolution (Powered By the Apocalypse or 4e). Bare minimum, DC 30+ should be "a thing" (truly impossible feats) and Success With a Cost should be much more than fail by 2 (Probably 5).
c) Rein in spell load-out proliferation (and recovery) and/or breadth in the last 10 levels a fair bit. Dungeon World martial characters are easily more versatile and more potent than their 5e counterparts. Dungeon World primary spellcasters have much, much, much less proliferate spell-casting than their 5e counterparts. Meanwhile, the game is beautifully balanced!
d) Give martial characters non-spellcasting moves that provide legitimate author stance capability in the Exploration and Social Pillars in the last two tiers of play.