Healing word smacks of magic, and Warlords are, from a narrative standpoint, expressly non-magical. For some that's not an issue, for some it is. I'm not going to exclude some by ignoring this aspect, nor tell people they have to ignore it for the game to work for them.
Magic Missile smacks of magic, too, but that doesn't stop anyone from using arrows. Cantrips take attack rolls and roll dice for damage, doesn't stop anyone from making attack rolls and rolling dice for damage with weapons (and vice versa).
The issue you're talking about is edition war hyperbole. No one will be excluded from the game by ignoring that invalid screed. Anyone honestly bothered by such things can just choose not to play Warlords, or, when playing Warlords, avoid those options that they've convinced themselves are problematic.
Marginalizing others concerns as rubbish is a bad way to approach designing a class. Not to mention that it's insulting.
Fans of Warlords are the ones who have been excluded, and would be marginalized by knuckling under to the unreasonable and irrational demands of edition war rhetoric that was never valid, and is now utterly irrelevant.
Just make sure that the 'objectionable' (ie, good/balanced/viable) choices have alternative options. Every class should have that much flexibility, really.
Marginalizing others concerns as rubbish is a bad way to approach designing a class.
As is paying attention to concerns that actually are rubbish. The edition war produced a lot of rubbish.
If you have advice or feedback on how to make a Warlord faithful to the concept, other than ignoring people's concerns, I'd love to hear your ideas.
Address their concerns by making the edition-war hot-botton features of the Warlord optional at the player level. That way they need never play a warlord with those features. If Inspiring Word is one of many choices, choosing something else is trivially easy.
It's a simple solution, entirely in line with 5e design philosophies. Even mechanics that aren't hot-buttons could do with such enlightened treatment.
On a side note, I really liked the idea of healing surges in 4e and do kind of feel that hit dice are underutilised in 5e. It could be a great resource for effects during combat, the fighter's second wind, for instance, could have been a power which enabled them to call upon their reserves and spend hit dice for self-healing in battle.
Yes, that would have been a more consistent design. But there was a great hew & cry from the usual suspects against HD during the playtest (because they are conceptually similar to surges). Instead of integrating HD into most hp-restoration sub-systems the way they were in 4e, and giving the game a firm foundation for day length in a fairly stable amount of available healing, /and/ providing a 'touch point' for modules that could, across the board, make the game 'grittier' or 'more epic' by restricting or enhancing healing, they isolated HD from other sub-systems so modules could constrict or eliminate them (and overnight healing), /without/ impacting the healing available from spells, potions and the like.
That's another unfortunate argument against using HD to fuel Inspiring Word. As elegant a possible solution as it may be when done well, it's not workable with modules meant to constrain or virtually eliminate non-magical healing be reducing HD, slowing their recovery, slowing natural healing, or eliminating the HD mechanic entirely. (It's not a very strong argument, because, really, why have a Warlord in campaign using such a magocentric module?)
[MENTION=59506]El Mahdi[/MENTION]: One take-away from all the above. Give players /options/ with your class or sub-classes. Don't hard-code in hp restoration or temp hps or any other mechanics (whether spurious objections were raised about them in the edition war or not) or specific concepts, but make your class & sub-classes /flexible/. There's a tremendous amount of versatility - at chargen, level-up, and even day-to-day, in most 5e classes. The Warlord, a leader, tactician, & strategist, needs to be designed to be resourceful and flexible. You can't just throw some big-number at him like you can the fighter and call it a day and expect to do the concept justice, let alone have a worthy successor to the original.