5e already includes all sorts of this sort of stuff (what's the narrative, in game justification for rogues being able to do things as a bonus action? how exactly does a barbarian's rage work, even to the point of resisting fire and lightning (depending on your totem)? how does that battlemaster make my character move farther than I possibly can?) and has from the get go. The greatest feat that 5e managed to pull off is convincing people that all those things they bitched about in 4e didn't exist in 5e.
It was never about those things. It was, I think, ultimately about balance. 4e classes were balanced, that was accomplished by greatly reigning in the versatility & power of spellcasters, and greatly expanding it for martial types. Mind you, the versatility of the arcane & divine classes was still greater than that of the martial, and martial was still the only pre-Essentials source to lack a controller, so it's not like it was ever perfect balance, or like the remaining imbalance wasn't still in favor of the usual suspects.
But it was as intolerable as complaining about it would have been unsympathetic, so we had all these stalking horses. Dumbed-down, too complicated; board game, too narrativist; dissociated mechanics; nerfed wizard; etc, etc...
But, come 5e, the magical classes are all there in partially-restored glory (and fewer limitations than ever) while non-magical sub-classes are few and DPR-focused (in a game tuned for /fast combat/), and the complaints vanish.
(iserth was right, I was sounding too bitter, now I feel I've properly expressed my cynicism, as well)
In my eyes, each edition does something extremely well.
1e - narrative immersion, homebrew imagination, opting into or out from rules
3e - systematization of rules, customizing an individual character
4e - gaming system balance, thematic rules: power types (arcane, primal, psionic, martial)
I appreciate the way 4e conceives types of power. Thinking about what ‘martial’ powers might be able to do, 4e expanded the possibilities for the fighter and the warlord.
There's also been a long pendulum-swing.
1e was extremely DM-Empowering, or, it might be more accurate to say, required the DM to seize that empowerment aggressively to be effective.
2e was more consistent, and gave players more options, but still left the DM tremendous latitude.
3.x is extremely player-empowering (I'll see if I can get away with that, or if someone will insist it was 'player entitlement'), with tremendous customizeability and equally lavish rewards for system mastery, and making DMing quite a chore.
4e was balanced and frequently added to & updated, pulling in system mastery rewards and making DMing surprisingly easy.
5e is extremely DM-Empowering again, calling for DM judgement constantly, and thus conditioning players to accept that judgement and angle for rewards from the DM, rather than from the system.