None of those were meant as examples of necessary Warlord tricks that couldn't be done, now. They were things a Warlord might do other than strict support-role functions - quite possibly in a few of the ways you describe, possibly in different ways using alternative uses/options to his support functions. That was in answer to Mouseferatu's question.
My point is, none of them for the most part can't be done NOW. Psionics is being added because its doing something the current casters can't yet do. What is the warlord going to add that a battlemaster with the proper skills and maneuvers can't do?
Did you just go all OneTrueWay, and threaten to resume edition war hostilities, before you got to the bit where the idea was not only optional, but more optional than anything had ever been optional in the history of gaming? (Not just 'DM table thing,' but /whole table unanimous consent required/)
And, no, not the basis of the class, just some oddball thing it might have when all the usual tricks don't apply.
No, I said that giving a warlord a plot coupon as a class feature will get it insta-banned from damn near everything but a select few groups. It changes not only the dynamic of the group, but the dynamic of the game itself. Imagine this.
DM: "Trapped by the drow! You are all prisoners in a drow camp!"
Warlord Player: "How'd we get here?"
DM: "...Well, you were on the surface and a drow raiding party ambushed you..."
Warlord Player: "Oh, because I have the Foil Ambush power, so they couldn't get surprise on us. Further, I use the Horn of Cormyr to call out for allies. Right now, a group of Purple Dragon Knights and their dwarven allies are searching for us; when they come we'll escape and all go back to the surface. I can do that because I have the "Call Allies in a crunch" plot coupon for being a warlord...
DM: "..."
Warlord Player: "Hey, when we get back to the surface, wanna go explore Waterdeep?"
Trust me, I don't care if you put giant hazard stickers, locked it on sealed pages between page 32 and 35, and had to sign a wavier to allow it; this ain't making it past playtesting for a normal class. Its a DM module, not a player class option.
Sure, the Warlord and BattleMaster will be able to do a lot of the same things. Just like the Wizard and the Eldritch Knight can do a lot of the same things. 5e has a lot of overlap, a lot of the exact same abilities shared among multiple classes.
So, aside from real healing, what does a warlord do that a battlemaster can't? I mean, a wizard can scry, fly, teleport, summon elementals, animate skeletons, beguile a creature's mind, making a fake door appear, or hurl meteors at the earth; the amount of overlap is fairly small between a wiz and an EK. for a warlord to exist on his own, he'd better be getting things of that magnitude vs a battlemaster's maneuvers...
So, we have on one side, the claim that the Warlord can't possibly be good enough to be viable. And, on the other (I think it was Chris), we have the claim that it can't help but be wildly overpowered.
Yeah, I said its a paradox. A class can simultaneously be too focused and too powerful. A warlord would almost have to be. If his powers are only on par with bless and healing word, for example, a cleric still has the advantage of casting divinations, protections, and utility magic where the warlord is useless unless he's granting a bonus to hit or healing hp. (At that point, a warlord is a cleric with only two fixed spell choices, for purposes of raw power). If you compensate for his lack of versatility by making his buffs better than a clerics (say, inspiring word is a long range d8 buff and inspiring action grants 1d6 to all allies) he's going to break the assumed power curve for a character of that level (aka the bounded accuracy).
The fear is that a warlord would be too good at his role (buffing and healing) to overcompensate for the fact he can't do what a spellcaster could do.
Here, you're insisting the Warlord cannot exist in 5e, because there is a Cleric/Druid/Bard-filled Role that is mandatory for the game, that the Warlord can't quite fill because he can't raise the dead (the other things you listed, could probably be dealt with somehow - he may not remove blindness, but maybe he could train the blinded character to compensate for it temporarily, for instance).
I'm suggesting that if given a choice, most people would want someone who can handle multiple different types of situations rather than hyperspecialize in just one. The latter runs the problem of "if all you have is a hammer..." syndrome. In essence, tell me why I would want Buffy McShoutheal over the guy who can buff, heal, divine, raise the dead, wind walk, allow us to breath in water, summon angels, etc.
Oh, a warlord can now cure blindness, even temporarily? Are we still aiming for "nonmagical", or are there examples of people being motivated to see again?
The simple fact remains that the Warlord was implemented very successfully in 4e, and that 5e gives greater freedom of design, making the successful implementation of the Warlord a shoe-in, if we could just, as a community, get past this bizarre need to dictate to eachother how we play the game, and let others have the options they want, and not be upset that others don't use the options we want.
I've said before I don't care if they make a warlord, but I'm failing to see a place where one exists beyond "it was in 4e".