Yes, it is. For pretty much every outright Warlord fan I've ever spoken to, healing is in fact a requirement. Hence why it's so terrifically infuriating when that's the first thing every proposal puts on the chopping block.
The Warlord needs to be able to fill the support slot, even in parties without a single person who can cast cure wounds or healing word. That means real, actual, honest-to-God healing. It may be less healing than what a Cleric or Bard could produce (in fact, by level 4-6, I would absolutely expect the Warlord to be simply outclassed for healing, unless said Warlord has actively and aggressively pursued being a really, really, really good healer--and even then he should be struggling to keep up.) But it can't be zero healing, "only THP healing," only damage prevention/mitigation, etc. Sufficient amounts of those things that could actually obviate the need for healing would be severely unbalanced--and would make any party that does have magical healing even worse than a party that had to rely on the Warlord alone.
The problem is: it's also quite easy to die in my experience. Especially in the earliest levels, and/or in parties that don't have magic. I would know. I am the (Celestial Warlock) healer of a mostly-5.0, partly-5.5e game (very kindly run by Hussar), and dear God do we need the healing Celestial brings. If it weren't for my spell slots and daily Healing Radiance dice, things would have gone significantly worse for the party...and we've also had to rely on something like 15+ healing potions on top of that.
Hit Dice help, sure. They are emphatically nowhere near enough to keep up with the allegedly-expected 6-8 combat encounters a day, doubly so once you've spent one night out in the field, since you only get back half your HD, not all of them. That's where the Warlord's stuff comes in. It helps keep people off the floor and still in the fight. Temporary hit points cannot do that. They do absolutely, positively nothing for someone unconscious. They don't even cause a person to stabilize.
It is, simply put, utterly non-negotiable that any 5e Warlord be able to provide at least some healing. It doesn't have to be much--I quite liked the idea of "recipient spends a Hit Die and adds the Warlord's Leadership modifier on top"--but it's gotta be something. Linking it to Hit Dice serves the double purpose of calling back to 4e's mechanics (even if 5e Hit Dice have only the thinnest superficial similarity to Healing Surges), and mollifies the rustled jimmies over "no-cost healing" or various other common martial-healing gripes.
See, that's my point here. Warlords should not be comparable to frontline Fighters/Paladins/etc., unless they've invested in doing so. They're tricksy, wily, clever bastards, who should be at a slight distance removed. Pushing too much automatic, inherent warrior-ness into the class is a huge part of why the Fighter chassis doesn't work. It closes off too much other, valid, interesting design space because the Fighter chassis is already so roided out guns-blazing for personal effort. You can't take away core class features, but you can add them in with subclasses (and, as another perk of the Warlock-style/"fractal" class model, "invocation"-type selected features can do this too.)
We already know Extra Attack can be a subclass-specific feature (see: Bard, Blade Pact), as can heavier armor (Cleric, and BG3 offers it to Rangers as well). It makes sense that at least one subclass of Warlord should truly be a front-line warrior, standing shoulder to shoulder with the Barbarian, Fighter, Ranger, and/or Paladin. Hence my mention of the "Vanguard" subclass getting +1 HP/class level the way Dragon Sorcerers do, and I'd add heavy armor on top of that.
By leaving those things for folks who want to specialize in full-on warrior badassery, we can give folks who like that stuff exactly what they're hoping for, without forcing EVERYONE to deal with that being baked in.