There is an approach to RPG design - with The Forge at the centre, but the ripples have reached pretty far by now (Marvel Heroic Roleplaying thanks Vincent Baker and Clinton R Nixon in its acknowledgements!) - which holds that every episode of play should be awesome; that every episode of play should deliver dramatic thrills. (When Ron Edwards talks about playing for "story now", the emphasis is not on "story", it's on "NOW!")
At least in my own experience, real life - the weeks between sessions, and the moments during sessions when people eat food or take other sorts of breaks - delivers the necessary downtime to make the pursuit of ingame drama at every opportunity desirable.
If I'm looking at a system, and I'm seeing that in order to get the awesome I'm going to have to game through hours of non-awesome - eg combats or traps that nickle-and-dime away the first third or half of PC hit points; calculating encumbrance, inventory etc - then I don't think I'm interested. Whatever pleasure I am able to get out of that sort of thing I can get solving crosswords by myself.
I agree, and generally feel the same way. Although, honestly, I haven't found any edition of D&D very good at this. While I am curious to try 4e again, based primarily on our discussions here, I find that the generally slow (real-world) pace of resolution and all the fiddly-bits to be a distraction/detraction from the awesome. (True in both WotC editions.) To be fair, there are also those who find the "Fantasy Logistics and Accounting" portion of the game to be exciting/rewarding. (Gods help me I dunno why, but they're there.

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More to the point. Lately I find that other systems, which began from the "Story Now" perspective and serve it wholeheartedly, have a tremendous advantage over D&D with its sacred cows in this regard. I've gotten a chance to try out the latest incarnation of FATE, with kids even, and it just rolls right past D&D. So much so that, to some extent, I've given up trying to fit D&D's square peg into that round hole. I'd much rather play a fantasy version of FATE or one of the MHRP hacks when I'm looking for that story. D&D still has a place in my heart (and my weekly schedule), because its much better at scratching a different itch.
So for me, the litmus is - when I look at this system can I see where it is going to deliver all awesome, all the time? And for me, the warlord in 4e was one marker of that. The very fact that the game has as part of its core build that class, with those abilities and that function, tells me something about what the game apsires to. (Whether it also meets its aspirations is important too - in my own experience 4e mostly does, though it's not without its flaws.)
I almost hate to say this, but...
For better or worse, I don't think that's even close to the primary design goals for Basic/Core 5e. To wit: I think they are going for a "just slightly more than a board game" basic dungeon-crawl. I'm conjecturing that from all that "essence of D&D" talk combined with their recent revelations of what the Basic game product will be. They seem to believe that they can tack on the rest of it (for any given value of "the rest of it") in optional modules....who knows for certain?
Side Note: I will invoke some possibly hot-button terms here out of necessity. I'm not trying denigrate any particular aspect of 4e or its playstyle(s). Rather, I'm trying to make a point about designing 5e in the wake of 4e.
One side-effect of that gambit which seems to have many 4e fans upset is that far less is being built right into the root of the system. However, I think they are forced to take that route. See, 4e has very tight table-presence (I don't even want to call it playstyle), particularly in combat. I've heard words like "gonzo fantasy", "cinematic", "super-heroic", "set-piece battles", and a lot of others used to describe it. I'm not a particular fan of any of those terms, but whatever-you-want-to-call-it, 4e is focused on making it happen. In part, not surprisingly, because it was built from the ground up to play to those conceits using a D&D framework. The numbers, the mechanics, and the interaction of the mechanics, are all tightly integrated and focused in that direction. I think you're right in saying that 4e does a great job of creating that sort of thing...that
particular sort of thing. I suspect that since they are trying to make 5e hit a far wider range of table-presence, they
can't start from such a tightly-knit root as 4e did. (Or perhaps they feel any such root would be essentially meaningless? - hard to tell.) Even if that's not the case, they have fairly plainly stated their belief that it's easier to create this variability through add-ons to a stripped-down core than re-building the core to different specifications. Which indicates that even if a more variable form of the 4e root
did exist, they have chosen not to make finding it their priority.
Of course just about all of that is pure speculation and conjecture.