I see nothing unreasonable in approaching a difficult problem with both confidence in the ability to understand the problem, and acknowledgement of one's own limitations when it comes to actually solving it. There's no contradiction there.
"cares about the integrity of the model" roughly means "treat the rules as the laws of phsysics for the imagined world, and assume the inhabitants of that world understand those laws & make decisions accordingly."
I did like the 2e 'Sphere' model, it made each priesthood more distinctive. Domains are not quite so versatile or interesting - but they are simpler and more focused.
He's always seemed very serious about believing himself the final arbiter of what is and is not really roleplaying.
Obviously, there was a way, since 4e did it, and it had very consistent rules, not in the least contorted. I think the important thing though, isn't whether they could do that again - they're professional game designers, some were even on the team that did it last time, give them a tiny bit of credit - but how they could do it /better/.
Inspiration, same as non-magical healing. defensive tactics, the warlord's maneuvers allow allies to sheild an ally and distract enemies so the subject escapes unscathed To disrupt casters? Perfectly timed missile fire. To prevent detection? Extraordinary preparation and execution of a diversion. Actually knowing the lore of the legend in question. extraordinary intuition/deduction It's hardly a support spell, anyway, is it? And blasting away with elements is no more Warlord-appropriate than grinding away with high DPR.
Again, this is a baseless assertion trivially disprove by the past success of the Warlord.
5e is not strictly inferior to 4e, just because 4e did it, doesn't mean 5e can't.
I think you're overestimating how inflexible warlord fans are. We want the option to play the class we liked in 4e. That class exists as an easy reference. What's more, it exists in only one iteration, so it is much easier to identify than any of the classes already designed for 4e.
Compare the state of the Warlord & it's fandom to that of psionics. Psionics has existed in 4 radically different forms: as a non-class random non-magical but superntural special ability steeped in Freudian and sci-fi terminology, as a single, wildly overpowered class using similar powers, to a number of classes using psionic powers that might, at the DM's option be magic or 'not magic,' to 4 classes, two similar, one somewhat different, one classic but never-before-psionic all explicitly using 'psionics' distinct from arcane, divine, or primal magic.
Yet, WotC hasn't shied away from putting psionics into the pipeline.
The Warlord has existed in one past edition, in one form. At least some of it's fans want it to grow beyond that.
No, that's really not much of a stumbling block.
And, I mean, seriously, what about the Ranger? The Ranger has that 'problem' worse than any class, it's the poster boy for no one really knows, let alone agrees, what it's really supposed to be.
Yet they tried to pull it together for the PH1, and are still trying out sub-classes, trying to come up with a few that stick.
As to how to please people with a variety of different visions of the same class? Sub-classes. Alternate class features. Options.
OK, this is nonsense. The Warlord is right there, in the 4e PH4. Fans differ on what they consider most important, and on what they might live without when pressed to 'make compromises' (why? with whom? in return for what?). Everything the Warlord was in 4e could be done in 5e.
5e is not some hobbled, strictly inferior version of D&D, it can do any class that 4e did, and probably do it better.