I apologize for my absence. My personal life has been pretty hectic the past few days. Only good news, I assure you. But also in the interest of time, plus my personal distaste of the Wall of Text internet art form, I hope you don't mind if I summarize your points.
Everyone has completely different ideas of what a shaman looks like: mythology, anthropological, like Warcraft's, like the shaman from 4e (similar to the spirit shaman from 3e), like Pathfinder's, like the 2e kit, etc.
The warlord is a very different beast. When people design warlords, they're not designing based on a concept or archetype, they're designing basing on the mechanics of a class. It's not "how can I make a tactical commander class using the 5e rules?" or "how can I emulate a squad leader or Aragorn?" it's "how can I port these rules into 5th Edition?" There's going to be less variance as there's less reinterpretation going on. Mostly shuffling of when abilities are gained based on personal priorities.
The Warlord is a "different beast"from the shaman's rich multiplicity of expression, but it is not far removed from the similar origins of other classes. The sorcerer and the warlock leapt to my mind almost immediately when reading your point here. The Sorcerer, for example, was not really designed around a mythological or fantasy archetype, but, instead, more around the thought-experiment of a "non-Vancian spontaneous caster." It was essentially created only to be an alt-Wizard mechanic. It was only later that they slapped on the "magical bloodlines" justification. Even then it was just a one-line bit of speculation: "Some sorcerers claim that the blood of dragons courses through their veins," and that's it. The idea of magical bloodlines would then be expanded as a concept less so in 3E itself, but in the competing Pathfinder and 4th Edition (e.g., dragon and wild magic). The Warlock was also created in 3E not so much around fantasy concept but in terms of "what if we played with this mechanic?", namely at-will magical blasting. There was nothing stopping you from roleplaying your wizard or sorcerer as a "warlock" before in 3E.
I think in part because the inspiration is single mechanical expression of the class rather than a narrative concept or multiple mechanical expressions across multiple editions, there's less room for variance. More people are making ultimatums regarding the warlord than something like the shaman: the warlord has to heal real hit points; it can't be a subclass; it has to be called the warlord; it has to be in a hardcover book used for AL; etc. For a while it had to grant attacks as an at-will power. There's tension points where there can be no compromise.
It's not enough for there to be a class that fills the same hook and does similar things.
Do you not think that this contention may also stem from hardliners on the opposing side of the fence? E.g., the warlord should not heal for real HP! the warlord cannot boost morale as that would communicate "relation" that should be covered by RP! I do not think that it is fair for either camp to portray this as a problem stemming from only the pro-warlord camp. It does a tremendous disservice to the complexity of the issues surrounding a possible implementation of the warlord.
As a weekend designer, I find that frustrating. If you're going to design a "tactical leader" class and make it awesome, why shackle your design to a dead edition? Take the concept and make it better. Find some new mechanics that wouldn't have worked in the AEDU chassis.
The point isn't to appeal to the small subset of existing D&D fans who liked something how it was mechanically done half a decade ago and are dissatisfied by current implementations, but to appeal to fans of the concept as a whole and do it better than before.
In this case, to design a warlord that doesn't just appeal to the nostalgia of 15-25% of ENWorld posters but to anyone who likes the idea of a tactical leader class/ subclass.
You are assuming several things here, namely that people are not attempting to better the concept for 5E. I know that Tony Vargas, for example, has been a huge advocate for expanding in 5E the focus of the Warlord beyond its restricted role scope and the AEDU system of 4E. In 4E terms, he has asked why the 5E Warlord should be restricted to what 4E would regard as the "leader" role. As for myself, I never could get fully on-board with 4E, though I did play it for several campaigns and appreciated what the edition attempted in its ambitious project. So, in some respects, I would consider myself more closely aligned with what you describe in your final sentence here. The 4E Warlord primarily succeeded in whetting my appetite for a tactical support/utility/control martial class. It is not the Warlord fans who shackle the class to a prior edition, but, rather, it is those who hope that it drowns to its death alongside the dead edition. Warlord fans want to liberate the class from its shackles so that it may experience reinvigorated life in a new edition. It is certainly ironic that you would cite Warlord nostalgia as something to be decried as a negative in an edition that regards nostalgia of prior editions as something worth lauding.
The 4E Warlord provides perhaps the most realized form, at least so far, of what you have described as the "tactical leader" in any edition. I do not think that it is the only source of inspiration people have been using either. As you say, you want something that would work within the framework of the 5E action economy that's balanced, robust, and flavorful. And, indeed, there have been people who have looked to and cited other sources of inspiration. This has been performed in terms of editions (e.g. the 3E Marshal, the 3E Bo9S's maneuvers and stances, even the 4E psionic Ardent), other tabletop RP games (e.g. Dreamscarred Press's Warlord or psionic Tactician for PF, the Commander for 13th Age, the Iron Heroes' Hunter, Arcana Evolved's Ritual Warrior, etc.), and fantasy/history/mythology (e.g. Odysseus, Julius Caesar, Zhuge Liang from Romance of the Three Kingdoms, Matrim Cauthon in Wheel of Time, Croaker in Black Company, etc.).
On "half-assing" and "demanding" the Warlord in 5e:
And - as mentioned above - there are the assorted requirements being placed on the design of the class. It's not enough that it feels like a walord and is balanced, it also has to do very specific things.
This is a highly contentious point of opinion, and one that should probably not be masqueraded as if it were a fact, as it is here. There are a number of Warlord fans who clearly do not think that the PDK or BM feel like a warlord, and they have expressed that opinion well enough. There are a number of reasons why they may feel that way: e.g., it feels too much like a fighter (too strong of an offensive DPR chassis) while not providing enough support/tactical play options, etc. But, in short, a lot of these so-called "5e warlords" that warlord-detractors point out woefully fall short of the idea that you described much earlier as what should be the goal: i.e. creating a "tactical leader." That's one reason why a number of "tactical leader" fans regard these implementations as half-assed. They simply don't fill the desired niche playstyle as what people have been wanting.
Now, in the few threads that have started as discussions on designing the warlord arguments do break out. But it's unfair to just blame "usual suspects who want to destroy any warlord project". It takes two to argue. If everyone in the thread was just working on designing the warlord, then the one or two posters who pop in and say "the warlord sux!" would stand out against the otherwise positive and constructive tone.
Things fall apart when the warlord fans engage with the detractors. They feed the trolls. Because the best (if not only) real defense of the warlord class is "because I like it." But defenders of the class break out other arguments to defend their personal tastes in class. But as these reasons are all debatable they're… well, debated.
I'm sorry, but this is nothing more than fallacious blaming the victim.