Kind of awesomely, such a module would even allow for non-magical clerics who could swap out high-special-FX god-sparkles for low-special-FX soothing words and consoling and the like....which is actually kind of right up the ally of a kind of character I'd like to play...but anyway...
I get you might not think such a thing is within the scope of 5e, and you may very well be right in that, but if it was? If 5e includes something like that, that would meet your needs, yes? Because then our only real disagreement is the very understandable one of, "Is 5e capable of this?"
If 5e turns out very differently from the playtest packets, and into a game that isn't Spellcasters Uber Alles and in which breaking open a heavy door or climbing a greased rope or breaking chains is possible for Asmodeus, and Legolas could reliably shield surf then I'd have some idea that it would work.
Hell, Tightrope walking in the current playtest packet is DC 25. I hate to think what the following youtube video in D&D Next would be. At least DC 30 and I think DC 35.
What skilled people in the real world can do without magic is much, much more awesome than anything in D&D Next's current playtest. DC25 for a simple walk across a tightrope? To take 10 (i.e. do it reliably), that means that every one of the above performers must be rolling at +15 (!). Meanwhile Fly is (as ever) a 3rd level spell.
While I'm at it, on a skim through. Drive. DC 15: Control a heavily laden cart on a steep descent. DC 20. Make a tight turn or steer round an obstacle. Handle Animal DC 30: Tame a Wild Animal. So someone with an 18 wisdom and skilled at animal handling needs a natural 20 and a natural 6. Sense Motive DC 25: Recognise an outside influence such as a spell on someone. That might as well be put in there to make sure people can't use skill to notice mind control magic. Keeping from getting lost in the wilderness is an improvised (i.e. no skill ) DC 20.
And the fighter gains no new capabilities after 11th level.
Yeah, no, this makes sense. It's totally fair and even I think really useful during a playtest period to be skeptical and to challenge the designers to show and not just tell.
As I've pointed out, the designers are showing. And what they are showing is non-magical people, other than having hides tougher than orc axes, can't even come close to matching up to real world levels of competence.
But the playtest isn't a preview, right?
The playtest is PR as much as anything. And what it shows us is what the designers are thinking. Right now they seem to be thinking the opposite way to you.
At any rate, the need for a specific warlord class seems to be something we can move past, into maybe how non-magical spike healing should be presented in 5e, or what you'd like out of a fast-healing or non-magical module for the game. I think you'd get a whole lot of agreement across all edition loyalties, that there should be a way to turn 5e into a game that doesn't require magical healing.
I'd hope so.
It's just a question about how likely la-la-land is to exist at that point. If the idea of a rules module in 5e that could include rules that remove the need for magical healing is fundamentally unbelievable to you, just come with me.
I see pointers at such a module all over previous editions, and what they've said in the material for 5e, too (L&L columns, for one). Living there, you'll be free, if you truly wish to be.
And I see pointers away from people without magic being useful other than to hold pointy bits of metal. See above. I prefer to remain bound by the evidence of my senses and my ability to understand what's going on.